Kyoto Journal of Mathematics Articles (Project Euclid)
http://projecteuclid.org/euclid.kjm
The latest articles from Kyoto Journal of Mathematics on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTFri, 22 Apr 2011 13:49 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
http://projecteuclid.org/
Toeplitz CAR flows and type I factorizations
http://projecteuclid.org/euclid.kjm/1271187735
<strong>Masaki Izumi</strong>, <strong>R. Srinivasan</strong><p><strong>Source: </strong>Kyoto J. Math., Volume 50, Number 1, 1--32.</p><p><strong>Abstract:</strong><br/>
Toeplitz CAR flows are a class of $E_{0}$ -semigroups including the first type III example constructed by R. T. Powers. We show that the Toeplitz CAR flows contain uncountably many mutually non-cocycle-conjugate $E_{0}$ -semigroups of type III. We also generalize the type III criterion for Toeplitz canonical anticommutation relation (CAR) flows employed by Powers (and later refined by W. Arveson), and show that Toeplitz CAR flows are always either of type I or type III.
</p>projecteuclid.org/euclid.kjm/1271187735_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTSpecifying the Auslander transpose in submodule category and its applicationshttps://projecteuclid.org/euclid.kjm/1543309295<strong>Abdolnaser Bahlekeh</strong>, <strong>Ali Mahin Fallah</strong>, <strong>Shokrollah Salarian</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 30 pages.</p><p><strong>Abstract:</strong><br/>
Let $(R,\mathfrak{m})$ be a $d$ -dimensional commutative Noetherian local ring. Let $\mathcal{M}$ denote the morphism category of finitely generated $R$ -modules, and let $\mathcal{S}$ be the full subcategory of $\mathcal{M}$ consisting of monomorphisms, known as the submodule category. This article reveals that the Auslander transpose in the category $\mathcal{S}$ can be described explicitly within $\operatorname{mod}R$ , the category of finitely generated $R$ -modules. This result is exploited to study the linkage theory as well as the Auslander–Reiten theory in $\mathcal{S}$ . In addition, motivated by a result of Ringel and Schmidmeier, we show that the Auslander–Reiten translations in the subcategories $\mathcal{H}$ and $\mathcal{G}$ , consisting of all morphisms which are maximal Cohen–Macaulay $R$ -modules and Gorenstein projective morphisms, respectively, may be computed within $\operatorname{mod}R$ via $\mathcal{G}$ -covers. The corresponding result for the subcategory of epimorphisms in $\mathcal{H}$ is also obtained.
</p>projecteuclid.org/euclid.kjm/1543309295_20190107220044Mon, 07 Jan 2019 22:00 ESTBundles of generalized theta functions over abelian surfaceshttps://projecteuclid.org/euclid.kjm/1540001287<strong>Dragos Oprea</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 42 pages.</p><p><strong>Abstract:</strong><br/>
We study the Verlinde bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree $0$ , the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors. Furthermore, Fourier–Mukai symmetries of the Verlinde bundles are found consistently with strange duality. Along the way, a transformation formula for the theta bundles is derived, extending a theorem of Drézet–Narasimhan from curves to abelian surfaces.
</p>projecteuclid.org/euclid.kjm/1540001287_20190107220044Mon, 07 Jan 2019 22:00 ESTThe balanced tensor product of module categorieshttps://projecteuclid.org/euclid.kjm/1538532153<strong>Christopher L. Douglas</strong>, <strong>Christopher Schommer-Pries</strong>, <strong>Noah Snyder</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 13 pages.</p><p><strong>Abstract:</strong><br/>
The balanced tensor product $M\otimes_{A}N$ of two modules over an algebra $A$ is the vector space corepresenting $A$ -balanced bilinear maps out of the product $M\times N$ . The balanced tensor product ${\mathcal{M}}\boxtimes_{\mathcal{C}}{\mathcal{N}}$ of two module categories over a monoidal linear category ${\mathcal{C}}$ is the linear category corepresenting ${\mathcal{C}}$ -balanced right-exact bilinear functors out of the product category ${\mathcal{M}}\times{\mathcal{N}}$ . We show that the balanced tensor product can be realized as a category of bimodule objects in ${\mathcal{C}}$ , provided the monoidal linear category is finite and rigid.
</p>projecteuclid.org/euclid.kjm/1538532153_20190107220044Mon, 07 Jan 2019 22:00 ESTIndex pairings for $\mathbb{R}^{n}$ -actions and Rieffel deformationshttps://projecteuclid.org/euclid.kjm/1534989636<strong>Andreas Andersson</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 47 pages.</p><p><strong>Abstract:</strong><br/>
With an action $\alpha$ of $\mathbb{R}^{n}$ on a $C^{*}$ -algebra $A$ and a skew-symmetric $n\times n$ matrix $\Theta$ , one can consider the Rieffel deformation $A_{\Theta}$ of $A$ , which is a $C^{*}$ -algebra generated by the $\alpha$ -smooth elements of $A$ with a new multiplication. The purpose of this article is to obtain explicit formulas for $K$ -theoretical quantities defined by elements of $A_{\Theta}$ . We give an explicit realization of the Thom class in $\mathit{KK}$ in any dimension $n$ and use it in the index pairings. For local index formulas we assume that there is a densely defined trace on $A$ , invariant under the action. When $n$ is odd, for example, we give a formula for the index of operators of the form $P\pi^{\Theta}(u)P$ , where $\pi^{\Theta}(u)$ is the operator of left Rieffel multiplication by an invertible element $u$ over the unitization of $A$ and $P$ is the projection onto the nonnegative eigenspace of a Dirac operator constructed from the action $\alpha$ . The results are new also for the undeformed case $\Theta=0$ . The construction relies on two approaches to Rieffel deformations in addition to Rieffel’s original one: Kasprzak deformation and warped convolution. We end by outlining potential applications in mathematical physics.
</p>projecteuclid.org/euclid.kjm/1534989636_20190107220044Mon, 07 Jan 2019 22:00 ESTCohomology for spatial superproduct systemshttps://projecteuclid.org/euclid.kjm/1534989637<strong>Oliver T. Margetts</strong>, <strong>R. Srinivasan</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 23 pages.</p><p><strong>Abstract:</strong><br/>
We introduce a cohomology theory for spatial superproduct systems and compute the $2$ -cocycles for some basic examples called Clifford superproduct systems , thereby distinguishing them up to isomorphism. This consequently proves that a family of $E_{0}$ -semigroups on type III factors, which we call CAR flows , are noncocycle-conjugate for different ranks. Similar results follow for the even CAR flows as well. We also compute the automorphism group of the Clifford superproduct systems.
</p>projecteuclid.org/euclid.kjm/1534989637_20190107220044Mon, 07 Jan 2019 22:00 ESTAffine surfaces with isomorphic $\mathbb{A}^{2}$ -cylindershttps://projecteuclid.org/euclid.kjm/1534838488<strong>Adrien Dubouloz</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 13 pages.</p><p><strong>Abstract:</strong><br/>
We show that all complements of cuspidal hyperplane sections of smooth projective cubic surfaces have isomorphic $\mathbb{A}^{2}$ -cylinders. As a consequence, we derive that the $\mathbb{A}^{2}$ -cancellation problem fails in every dimension greater than or equal to $2$ .
</p>projecteuclid.org/euclid.kjm/1534838488_20190107220044Mon, 07 Jan 2019 22:00 ESTFat-wedge filtration and decomposition of polyhedral productshttps://projecteuclid.org/euclid.kjm/1532743573<strong>Kouyemon Iriye</strong>, <strong>Daisuke Kishimoto</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 51 pages.</p><p><strong>Abstract:</strong><br/>
The polyhedral product constructed from a collection of pairs of cones and their bases and a simplicial complex $K$ is studied by investigating its filtration called the fat-wedge filtration . We give a sufficient condition for decomposing the polyhedral product in terms of the fat-wedge filtration of the real moment-angle complex for $K$ , which is a desuspension of the decomposition of the suspension of the polyhedral product due to Bahri, Bendersky, Cohen, and Gitler. We show that the condition also implies a strong connection with the Golodness of $K$ , and it is satisfied when $K$ is dual sequentially Cohen–Macaulay over $\mathbb{Z}$ or $\lceil\frac{\dim K}{2}\rceil$ -neighborly so that the polyhedral product decomposes. Specializing to the moment-angle complex, we prove that the similar condition on its fat-wedge filtrations is necessary and sufficient for its decomposition.
</p>projecteuclid.org/euclid.kjm/1532743573_20190107220044Mon, 07 Jan 2019 22:00 ESTExtending properties to relatively hyperbolic groupshttps://projecteuclid.org/euclid.kjm/1547802013<strong>Daniel A. Ramras</strong>, <strong>Bobby W. Ramsey</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 14 pages.</p><p><strong>Abstract:</strong><br/>
Consider a finitely generated group $G$ that is relatively hyperbolic with respect to a family of subgroups $H_{1},\ldots,H_{n}$ . We present an axiomatic approach to the problem of extending metric properties from the subgroups $H_{i}$ to the full group $G$ . We use this to show that both (weak) finite decomposition complexity and straight finite decomposition complexity are extendable properties. We also discuss the equivalence of two notions of straight finite decomposition complexity.
</p>projecteuclid.org/euclid.kjm/1547802013_20190118040045Fri, 18 Jan 2019 04:00 ESTTwo applications of strong hyperbolicityhttps://projecteuclid.org/euclid.kjm/1549270868<strong>Bogdan Nica</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 10 pages.</p><p><strong>Abstract:</strong><br/>
We present two analytic applications of the fact that a hyperbolic group can be endowed with a strongly hyperbolic metric. The first application concerns the crossed product $C^{*}$ -algebra defined by the action of a hyperbolic group on its boundary. We construct a natural time flow, involving the Busemann cocycle on the boundary. This flow has a natural KMS state, coming from the Hausdorff measure on the boundary, which is furthermore unique when the group is torsion-free. The second application is a short new proof of the fact that a hyperbolic group admits a proper isometric action on an $\ell ^{p}$ -space for large enough $p$ .
</p>projecteuclid.org/euclid.kjm/1549270868_20190204040138Mon, 04 Feb 2019 04:01 ESTConstructing MASAs with prescribed propertieshttps://projecteuclid.org/euclid.kjm/1551236641<strong>Sorin Popa</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 31 pages.</p><p><strong>Abstract:</strong><br/>
We consider an iterative procedure for constructing maximal abelian $^{*}$ -subalgebras (MASAs) satisfying prescribed properties in II $_{1}$ factors. This method pairs well with the intertwining by bimodules technique and with properties of the MASA and of the ambient factor that can be described locally. We obtain such a local characterization for II $_{1}$ factors $M$ that have an s-MASA , $A\subset M$ (i.e., for which $A\veeJAJ$ is maximal abelian in $\mathcal {B}(L^{2}M)$ ), and use this strategy to prove that any factor in this class has uncountably many nonintertwinable singular (resp., semiregular) s-MASAs.
</p>projecteuclid.org/euclid.kjm/1551236641_20190226220456Tue, 26 Feb 2019 22:04 ESTProjective unitary representations of infinite-dimensional Lie groupshttps://projecteuclid.org/euclid.kjm/1554170605<strong>Bas Janssens</strong>, <strong>Karl-Hermann Neeb</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 2, 293--341.</p><p><strong>Abstract:</strong><br/>
For an infinite-dimensional Lie group $G$ modeled on a locally convex Lie algebra ${\mathfrak{g}}$ , we prove that every smooth projective unitary representation of $G$ corresponds to a smooth linear unitary representation of a Lie group extension $G^{\sharp}$ of $G$ . (The main point is the smooth structure on $G^{\sharp}$ .) For infinite-dimensional Lie groups $G$ which are $1$ -connected, regular, and modeled on a barreled Lie algebra ${\mathfrak{g}}$ , we characterize the unitary ${\mathfrak{g}}$ -representations which integrate to $G$ . Combining these results, we give a precise formulation of the correspondence between smooth projective unitary representations of $G$ , smooth linear unitary representations of $G^{\sharp}$ , and the appropriate unitary representations of its Lie algebra ${\mathfrak{g}}^{\sharp}$ .
</p>projecteuclid.org/euclid.kjm/1554170605_20190527040153Mon, 27 May 2019 04:01 EDTUniform K-stability and plt blowups of log Fano pairshttps://projecteuclid.org/euclid.kjm/1555660964<strong>Kento Fujita</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 2, 399--418.</p><p><strong>Abstract:</strong><br/>
We show relationships between uniform K-stability and plt blowups of log Fano pairs. We see that it is enough to evaluate certain invariants defined by volume functions for all plt blowups in order to test the uniform K-stability of log Fano pairs. We also discuss the uniform K-stability of two log Fano pairs under crepant finite covers. Moreover, we give another proof of the K-semistability of the projective plane.
</p>projecteuclid.org/euclid.kjm/1555660964_20190527040153Mon, 27 May 2019 04:01 EDTOn $n$ -dimensional fractional Hardy operators and commutators in variable Herz-type spaceshttps://projecteuclid.org/euclid.kjm/1555660963<strong>Liwei Wang</strong>, <strong>Meng Qu</strong>, <strong>Wenyu Tao</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 2, 419--439.</p><p><strong>Abstract:</strong><br/>
Based on the theory of variable exponents and atomic decomposition, we study the boundedness of $n$ -dimensional fractional Hardy operators on variable Herz and Herz-type Hardy spaces, where the three main indices are variable exponents. The corresponding boundedness for the $m$ th order commutators generated by the $n$ -dimensional fractional Hardy operators and bounded mean oscillation (BMO) function are also considered. We note that, even in the special case of $m=1$ , the obtained results are also new.
</p>projecteuclid.org/euclid.kjm/1555660963_20190527040153Mon, 27 May 2019 04:01 EDTOn some spectral properties of the weighted $\overline{\partial}$ -Neumann operatorhttps://projecteuclid.org/euclid.kjm/1556330547<strong>Franz Berger</strong>, <strong>Friedrich Haslinger</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 2, 441--453.</p><p><strong>Abstract:</strong><br/>
We study necessary conditions for compactness of the weighted $\overline{\partial}$ -Neumann operator on the space $L^{2}(\mathbb{C}^{n},e^{-\varphi})$ for a plurisubharmonic function $\varphi$ . Under the assumption that the corresponding weighted Bergman space of entire functions has infinite dimension, a weaker result is obtained by simpler methods. Moreover, we investigate (non)compactness of the $\overline{\partial}$ -Neumann operator for decoupled weights, which are of the form $\varphi(z)=\varphi_{1}(z_{1})+\cdots +\varphi_{n}(z_{n})$ . More can be said if every $\Delta\varphi_{j}$ defines a nontrivial doubling measure.
</p>projecteuclid.org/euclid.kjm/1556330547_20190527040153Mon, 27 May 2019 04:01 EDTAngehrn–Siu type effective basepoint freeness for quasi-log canonical pairshttps://projecteuclid.org/euclid.kjm/1557216017<strong>Haidong Liu</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 2, 455--470.</p><p><strong>Abstract:</strong><br/>
We prove Angehrn–Siu type effective freeness and effective point separation for quasi-log canonical pairs. As a natural consequence, we obtain that these two results hold for semi-log canonical pairs. One of the main ingredients of our proof is inversion of adjunction for quasi-log canonical pairs, which is established in this paper.
</p>projecteuclid.org/euclid.kjm/1557216017_20190527040153Mon, 27 May 2019 04:01 EDTThe notion of cusp forms for a class of reductive symmetric spaces of split rank $1$https://projecteuclid.org/euclid.kjm/1557367351<strong>Erik P. van den Ban</strong>, <strong>Job J. Kuit</strong>, <strong>Henrik Schlichtkrull</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 2, 471--513.</p><p><strong>Abstract:</strong><br/>
We study a notion of cusp forms for the symmetric spaces $G/H$ with $G=\mathrm{SL}(n,{\mathbb{R}})$ and $H=\mathrm{S}(\mathrm{GL}(n-1,{\mathbb{R}})\times \mathrm{GL}(1,{\mathbb{R}}))$ . We classify all minimal parabolic subgroups of $G$ for which the associated cuspidal integrals are convergent and discuss the possible definitions of cusp forms. Finally, we show that the closure of the direct sum of the discrete series representations of $G/H$ coincides with the space of cusp forms.
</p>projecteuclid.org/euclid.kjm/1557367351_20190527040153Mon, 27 May 2019 04:01 EDTExplicit description of jumping phenomena on moduli spaces of parabolic connections and Hilbert schemes of points on surfaceshttps://projecteuclid.org/euclid.kjm/1563242599<strong>Arata Komyo</strong>, <strong>Masa-Hiko Saito</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 515--552.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate the apparent singularities and the dual parameters of rank $2$ parabolic connections on $\mathbb{P}^{1}$ and rank $2$ (parabolic) Higgs bundles on $\mathbb{P}^{1}$ . Then we obtain explicit descriptions of Zariski-open sets of the moduli space of the parabolic connections and the moduli space of the Higgs bundles. For $n=5$ , we can give global descriptions of the moduli spaces in detail.
</p>projecteuclid.org/euclid.kjm/1563242599_20190807040132Wed, 07 Aug 2019 04:01 EDTA fractional calculus approach to rough integrationhttps://projecteuclid.org/euclid.kjm/1558059097<strong>Yu Ito</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 553--573.</p><p><strong>Abstract:</strong><br/>
On the basis of fractional calculus, we introduce an integral of controlled paths against $\beta $ -Hölder rough paths with $\beta \in (1/3,1/2]$ . The integral is defined by the Lebesgue integrals for fractional derivative operators, without using any argument based on discrete approximation. We show in this article that the integral is consistent with that obtained by the usual integration in rough path analysis, given by the limit of the compensated Riemann–Stieltjes sums.
</p>projecteuclid.org/euclid.kjm/1558059097_20190807040132Wed, 07 Aug 2019 04:01 EDTCotorsion pairs in categories of quiver representationshttps://projecteuclid.org/euclid.kjm/1556157622<strong>Henrik Holm</strong>, <strong>Peter Jørgensen</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 575--606.</p><p><strong>Abstract:</strong><br/>
We study the category $\operatorname{Rep}(Q,\mathcal{M})$ of representations of a quiver $Q$ with values in an abelian category $\mathcal{M}$ . Under certain assumptions, we show that every cotorsion pair $(\mathcal{A},\mathcal{B})$ in $\mathcal{M}$ induces two (explicitly described) cotorsion pairs $(\Phi (\mathcal{A}),\operatorname{Rep}(Q,\mathcal{B}))$ and $(\operatorname{Rep}(Q,\mathcal{A}),\Psi (\mathcal{B}))$ in $\operatorname{Rep}(Q,\mathcal{M})$ . This is akin to a result by Gillespie, which asserts that a cotorsion pair $(\mathcal{A},\mathcal{B})$ in $\mathcal{M}$ induces cotorsion pairs $(\widetilde{\mathcal{A}},\operatorname{dg}\widetilde{\mathcal{B}})$ and $(\operatorname{dg}\widetilde{\mathcal{A}},\widetilde{\mathcal{B}})$ in the category $\operatorname{Ch}(\mathcal{M})$ of chain complexes in $\mathcal{M}$ . Special cases of our results recover descriptions of the projective and injective objects in $\operatorname{Rep}(Q,\mathcal{M})$ proved by Enochs, Estrada, and García Rozas.
</p>projecteuclid.org/euclid.kjm/1556157622_20190807040132Wed, 07 Aug 2019 04:01 EDTA local rigidity theorem for finite actions on Lie groups and application to compact extensions of $\mathbb{R}^{n}$https://projecteuclid.org/euclid.kjm/1560218486<strong>Ali Baklouti</strong>, <strong>Souhail Bejar</strong>, <strong>Ramzi Fendri</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 607--618.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a Lie group, and let $\Gamma$ be a finite group. We show in this article that the space $\operatorname{Hom}(\Gamma ,G)/G$ is discrete and—in addition—finite if $G$ has finitely many connected components. This means that in the case in which $\Gamma$ is a discontinuous group for the homogeneous space $G/H$ , where $H$ is a closed subgroup of $G$ , all the elements of Kobayashi’s parameter space are locally rigid. Equivalently, any Clifford–Klein form of finite fundamental group does not admit nontrivial continuous deformations. As an application, we provide a criterion of local rigidity in the context of compact extensions of $\mathbb{R}^{n}$ .
</p>projecteuclid.org/euclid.kjm/1560218486_20190807040132Wed, 07 Aug 2019 04:01 EDTExplicit calculation of local integrals for twisted triple product $L$ -functionshttps://projecteuclid.org/euclid.kjm/1558145160<strong>Isao Ishikawa</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 619--648.</p><p><strong>Abstract:</strong><br/>
Ichino proved a formula expressing global trilinear period integrals as products of central values of triple product $L$ -functions and certain local trilinear integrals. In general, these local trilinear integrals are difficult to evaluate, and the main result in this article is to prove an identity relating local trilinear integrals and products of local Rankin–Selberg integrals in the twisted case. This result has applications to an explicit version of Ichino’s formula and the construction of $p$ -adic $L$ -functions for twisted triple products in our forthcoming works.
</p>projecteuclid.org/euclid.kjm/1558145160_20190807040132Wed, 07 Aug 2019 04:01 EDTSpin networks, Ehrhart quasipolynomials, and combinatorics of dormant indigenous bundleshttps://projecteuclid.org/euclid.kjm/1562032985<strong>Yasuhiro Wakabayashi</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 649--684.</p><p><strong>Abstract:</strong><br/>
It follows from work of S. Mochizuki, F. Liu, and B. Osserman that there is a relationship between Ehrhart’s theory concerning rational polytopes and the geometry of the moduli stack classifying dormant indigenous bundles on a proper hyperbolic curve in positive characteristic. This relationship was established by considering the (finite) cardinality of the set consisting of certain colorings on a $3$ -regular graph called spin networks . In the present article, we recall the correspondences between spin networks, lattice points of rational polytopes, and dormant indigenous bundles and present some identities and explicit computations of invariants associated with the objects involved.
</p>projecteuclid.org/euclid.kjm/1562032985_20190807040132Wed, 07 Aug 2019 04:01 EDTDeformation equivalence classes of Inoue surfaces with $b_{1}=1$ and $b_{2}=0$https://projecteuclid.org/euclid.kjm/1558145161<strong>Shota Murakami</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 685--701.</p><p><strong>Abstract:</strong><br/>
In this article, we will show that if $S$ is an Inoue surface with $b_{1}=1$ and $b_{2}=0$ , then the number of deformation equivalence classes of complex surfaces diffeomorphic to $S$ is at most $16$ .
</p>projecteuclid.org/euclid.kjm/1558145161_20190807040132Wed, 07 Aug 2019 04:01 EDTSmall embeddings of integral domainshttps://projecteuclid.org/euclid.kjm/1558404168<strong>Yu Yang Bao</strong>, <strong>Daniel Daigle</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 703--716.</p><p><strong>Abstract:</strong><br/>
Let $A$ be a geometrically integral algebra over a field $k$ . We prove that, for any affine $k$ -domain $R$ , if there exists an extension field $K$ of $k$ such that $R\subseteq K\otimes_{k}A$ and $R\nsubseteq K$ , then there exists an extension field $L$ of $k$ such that $R\subseteqL\otimes_{k}A$ and $\operatorname{trdeg}_{k}(L)\lt \operatorname{trdeg}_{k}(R)$ . This generalizes a result of Freudenburg, namely, the fact that this is true for $A=k^{[1]}$ .
</p>projecteuclid.org/euclid.kjm/1558404168_20190807040132Wed, 07 Aug 2019 04:01 EDTKolyvagin systems and Iwasawa theory of generalized Heegner cycleshttps://projecteuclid.org/euclid.kjm/1562896995<strong>Matteo Longo</strong>, <strong>Stefano Vigni</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 717--746.</p><p><strong>Abstract:</strong><br/>
Iwasawa theory of Heegner points on abelian varieties of $\operatorname{GL}_{2}$ type has been studied by, among others, Mazur, Perrin-Riou, Bertolini, and Howard. The purpose of this article is to describe extensions of some of their results in which abelian varieties are replaced by the Galois cohomology of Deligne’s $p$ -adic representation attached to a modular form of even weight greater than $2$ . In this setting, the role of Heegner points is played by higher-dimensional Heegner-type cycles that have been recently defined by Bertolini, Darmon, and Prasanna. Our results should be compared with those obtained, via deformation-theoretic techniques, by Fouquet in the context of Hida families of modular forms.
</p>projecteuclid.org/euclid.kjm/1562896995_20190807040132Wed, 07 Aug 2019 04:01 EDTCanonical singularities of dimension three in characteristic $2$ which do not follow Reid’s ruleshttps://projecteuclid.org/euclid.kjm/1563328865<strong>Masayuki Hirokado</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 4, 747--768.</p><p><strong>Abstract:</strong><br/>
We continue studying compound Du Val singularities defined over an algebraically closed field $k$ , and present concrete examples in characteristic $2$ which have one-dimensional singular loci but do not admit a description as a trivial product (a rational double point) $\times $ (a curve) up to analytic isomorphism at any point. Unlike in other characteristics, we find a large number of such examples whose general hyperplane sections have rational double points of type $D$ . These compound Du Val singularities shall be viewed as a special class of canonical singularities. In the previous work with Ito and Saito, we classified such singularities in $p\geq 3$ ,
and I intend to complete our classification in arbitrary characteristic, reinforcing Reid’s result in characteristic $0$ .
</p>projecteuclid.org/euclid.kjm/1563328865_20191115220155Fri, 15 Nov 2019 22:01 ESTOn the almost Gorenstein property in the Rees algebras of contracted idealshttps://projecteuclid.org/euclid.kjm/1571904147<strong>Shiro Goto</strong>, <strong>Naoyuki Matsuoka</strong>, <strong>Naoki Taniguchi</strong>, <strong>Ken-ichi Yoshida</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 4, 769--785.</p><p><strong>Abstract:</strong><br/>
We explore the question of when the Rees algebra $\mathcal{R}(I)=\bigoplus_{n\ge0}I^{n}$ of $I$ is an almost Gorenstein graded ring, where $R$ is a 2-dimensional regular local ring and $I$ is a contracted ideal of $R$ . Recently, we showed that $\mathcal{R}(I)$ is an almost Gorenstein graded ring for every integrally closed ideal $I$ of $R$ . The main results of the present article show that if $I$ is a contracted ideal with $\mathrm{o}(I)\le2$ , then $\mathcal{R}(I)$ is an almost Gorenstein graded ring, while if $\mathrm{o}(I)\ge3$ , then $\mathcal{R}(I)$ is not necessarily an almost Gorenstein graded ring, even though $I$ is a contracted stable ideal. Thus both affirmative and negative answers are given.
</p>projecteuclid.org/euclid.kjm/1571904147_20191115220155Fri, 15 Nov 2019 22:01 ESTOn the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebrashttps://projecteuclid.org/euclid.kjm/1569376962<strong>Haian He</strong>, <strong>Toshihisa Kubo</strong>, <strong>Roger Zierau</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 4, 787--813.</p><p><strong>Abstract:</strong><br/>
In this article, we explicitly list all reducible scalar-type generalized Verma modules for all maximal parabolic subalgebras of the simple complex Lie algebras.
</p>projecteuclid.org/euclid.kjm/1569376962_20191115220155Fri, 15 Nov 2019 22:01 ESTThin $\mathrm{II}_{1}$ factors with no Cartan subalgebrashttps://projecteuclid.org/euclid.kjm/1569463628<strong>Anna Sofie Krogager</strong>, <strong>Stefaan Vaes</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 4, 815--867.</p><p><strong>Abstract:</strong><br/>
It is a wide open problem to give an intrinsic criterion for a $\mathrm{II}_{1}$ factor $M$ to admit a Cartan subalgebra $A$ . When $A\subset M$ is a Cartan subalgebra, the $A$ -bimodule $L^{2}(M)$ is simple in the sense that the left and right actions of $A$ generate a maximal abelian subalgebra of $B(L^{2}(M))$ . A $\mathrm{II}_{1}$ factor $M$ that admits such a subalgebra $A$ is said to be $s$ -thin. Very recently, Popa discovered an intrinsic local criterion for a $\mathrm{II}_{1}$ factor $M$ to be $s$ -thin and left open the question whether all $s$ -thin $\mathrm{II}_{1}$ factors admit a Cartan subalgebra. We answer this question negatively by constructing $s$ -thin $\mathrm{II}_{1}$ factors without Cartan subalgebras.
</p>projecteuclid.org/euclid.kjm/1569463628_20191115220155Fri, 15 Nov 2019 22:01 ESTA nonlinear theory of infrahyperfunctionshttps://projecteuclid.org/euclid.kjm/1569484831<strong>Andreas Debrouwere</strong>, <strong>Hans Vernaeve</strong>, <strong>Jasson Vindas</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 4, 869--895.</p><p><strong>Abstract:</strong><br/>
We develop a nonlinear theory for infrahyperfunctions (also referred to as quasianalytic (ultra)distributions by L. Hörmander). In the hyperfunction case, our work can be summarized as follows. We construct a differential algebra that contains the space of hyperfunctions as a linear differential subspace and in which the multiplication of real analytic functions coincides with their ordinary product. Moreover, by proving an analogue of Schwartz’s impossibility result for hyperfunctions, we show that this embedding is optimal. Our results fully solve an earlier question raised by M. Oberguggenberger.
</p>projecteuclid.org/euclid.kjm/1569484831_20191115220155Fri, 15 Nov 2019 22:01 ESTGushel–Mukai varieties: Linear spaces and periodshttps://projecteuclid.org/euclid.kjm/1569484830<strong>Olivier Debarre</strong>, <strong>Alexander Kuznetsov</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 4, 897--953.</p><p><strong>Abstract:</strong><br/>
Beauville and Donagi proved in 1985 that the primitive middle cohomology of a smooth complex cubic $4$ -fold and the primitive second cohomology of its variety of lines, a smooth hyper-Kähler $4$ -fold, are isomorphic as polarized integral Hodge structures. We prove analogous statements for smooth complex Gushel–Mukai varieties of dimension $4$ (resp., $6$ ), that is, smooth dimensionally transverse intersections of the cone over the Grassmannian $\mathsf{Gr}(2,5)$ , a quadric, and two hyperplanes (resp., of the cone over $\mathsf{Gr}(2,5)$ and a quadric). The associated hyper-Kähler $4$ -fold is in both cases a smooth double cover of a hypersurface in ${\mathbf{P}}^{5}$ called an Eisenbud–Popescu–Walter sextic.
</p>projecteuclid.org/euclid.kjm/1569484830_20191115220155Fri, 15 Nov 2019 22:01 ESTA Fock space model for decomposition numbers for quantum groups at roots of unityhttps://projecteuclid.org/euclid.kjm/1571731341<strong>Martina Lanini</strong>, <strong>Arun Ram</strong>, <strong>Paul Sobaje</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 4, 955--991.</p><p><strong>Abstract:</strong><br/>
In this paper we construct an abstract Fock space for general Lie types that serves as a generalization of the infinite wedge $q$ -Fock space familiar in type A. Specifically, for each positive integer $\ell $ , we define a $\mathbb{Z}[q,q^{-1}]$ -module $\mathcal{F}_{\ell }$ with bar involution by specifying generators and straightening relations adapted from those appearing in the Kashiwara–Miwa–Stern formulation of the $q$ -Fock space. By relating $\mathcal{F}_{\ell }$ to the corresponding affine Hecke algebra, we show that the abstract Fock space has standard and canonical bases for which the transition matrix produces parabolic affine Kazhdan–Lusztig polynomials. This property and the convenient combinatorial labeling of bases of $\mathcal{F}_{\ell }$ by dominant integral weights makes $\mathcal{F}_{\ell }$ a useful combinatorial tool for determining decomposition numbers of Weyl modules for quantum groups at roots of unity.
</p>projecteuclid.org/euclid.kjm/1571731341_20191115220155Fri, 15 Nov 2019 22:01 ESTMultidimensional continued fractions for cyclic quotient singularities and Dedekind sumshttps://projecteuclid.org/euclid.kjm/1565402423<strong>Tadashi Ashikaga</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 4, 993--1039.</p><p><strong>Abstract:</strong><br/>
We present a multidimensional continued fraction of Hirzebruch–Jung type which controls a certain resolution of an isolated cyclic quotient singularity, and we study its geometric properties. As an application, we explicitly express a certain $3$ -dimensional Fourier–Dedekind sum in terms of our continued fraction.
</p>projecteuclid.org/euclid.kjm/1565402423_20191115220155Fri, 15 Nov 2019 22:01 ESTLog-canonical degenerations of del Pezzo surfaces in $\mathbb{Q}$ -Gorenstein familieshttps://projecteuclid.org/euclid.kjm/1565402426<strong>Yuri Prokhorov</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 4, 1041--1073.</p><p><strong>Abstract:</strong><br/>
We classify del Pezzo surfaces of Picard number $1$ with log-canonical singularities admitting $\mathbb{Q}$ -Gorenstein smoothings.
</p>projecteuclid.org/euclid.kjm/1565402426_20191115220155Fri, 15 Nov 2019 22:01 ESTLocal theta lift for $p$ -adic unitary dual pairs $\mathrm{U}(2)\times \mathrm{U}(1)$ and $\mathrm{U}(2)\times \mathrm{U}(3)$https://projecteuclid.org/euclid.kjm/1569376961<strong>Yasuhiko Ikematsu</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 4, 1075--1110.</p><p><strong>Abstract:</strong><br/>
In this paper we describe the local theta lift for $p$ -adic unitary dual pairs $\mathrm{U}(2)\times\mathrm{U}(1)$ and $\mathrm{U}(2)\times \mathrm{U}(3)$ . We also describe the local theta lift for a pair of $p$ -adic quaternionic unitary groups of rank $1$ .
</p>projecteuclid.org/euclid.kjm/1569376961_20191115220155Fri, 15 Nov 2019 22:01 ESTAuslander’s formula: Variations and applicationshttps://projecteuclid.org/euclid.kjm/1578474089<strong>Javad J. Asadollahi</strong>, <strong>Najmeh N. Asadollahi</strong>, <strong>Rasool Hafezi</strong>, <strong>Razieh Vahed</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 31 pages.</p><p><strong>Abstract:</strong><br/>
According to Auslander’s formula, one way of studying an abelian category $\mathcal{C}$ is to study ${\mathrm{{mod\mbox{-}}}}\mathcal{C}$ , which has nicer homological properties than $\mathcal{C}$ , and then translate the results back to $\mathcal{C}$ . Recently, Krause gave a derived version of this formula and thus renewed the subject. This paper contains a detailed study of various versions of Auslander’s formula, including the versions for all modules and for unbounded derived categories. We also include some results concerning recollements of triangulated categories.
</p>projecteuclid.org/euclid.kjm/1578474089_20200108040156Wed, 08 Jan 2020 04:01 ESTHomogeneous Besov spaceshttps://projecteuclid.org/euclid.kjm/1576638468<strong>Yoshihiro Sawano</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 43 pages.</p><p><strong>Abstract:</strong><br/>
This note is based on a series of lectures delivered at Kyoto University in 2015. This note surveys the homogeneous Besov space $\dot{B}^{s}_{pq}$ on ${\mathbb{R}}^{n}$ with $1\le p$ , $q\le \infty $ and $s\in {\mathbb{R}}$ in a rather self-contained manner. Among other results, we show that ${\mathcal{S}}'_{\infty }$ and ${\mathcal{S}}'/{\mathcal{P}}$ are isomorphic, and we also discuss the realizations in $\dot{B}^{s}_{pq}$ . The fact that ${\mathcal{S}}'_{\infty }$ and ${\mathcal{S}}'/{\mathcal{P}}$ are isomorphic can be found in textbooks. The realization of $\dot{B}^{s}_{pq}$ can be found in works by Bahouri, Chemin, and Danchin and by Bourdaud for example. Here, we prove these facts using fundamental results in functional analysis such as the Hahn–Banach extension theorem.
</p>projecteuclid.org/euclid.kjm/1576638468_20200108040156Wed, 08 Jan 2020 04:01 ESTBlurred combinatorics in resolution of singularities: (a little) beyond the characteristic polytopehttps://projecteuclid.org/euclid.kjm/1575515303<strong>Helena Cobo</strong>, <strong>M. J. Soto</strong>, <strong>José M. Tornero</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 21 pages.</p><p><strong>Abstract:</strong><br/>
We introduce a variation of the well-known Newton–Hironaka polytope for algebroid hypersurfaces. This combinatorial object is a perturbed version of the original one, parameterized by a real number $\varepsilon \in {\mathbb{R}}_{\geq 0}$ . For well-chosen values of the parameter, the objects obtained are very close to the original, while at the same time presenting more (hopefully interesting) information in a way that does not depend on the choice of parameter.
</p>projecteuclid.org/euclid.kjm/1575515303_20200108040156Wed, 08 Jan 2020 04:01 ESTDerived categories of Artin–Mumford double solidshttps://projecteuclid.org/euclid.kjm/1575515304<strong>Shinobu Hosono</strong>, <strong>Hiromichi Takagi</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 71 pages.</p><p><strong>Abstract:</strong><br/>
We consider the derived category of an Artin–Mumford quartic double solid blown up at $10$ ordinary double points. We show that it has a semiorthogonal decomposition containing the derived category of the Enriques surface of a Reye congruence. This answers affirmatively a conjecture by Ingalls and Kuznetsov.
</p>projecteuclid.org/euclid.kjm/1575515304_20200108040156Wed, 08 Jan 2020 04:01 ESTThe étale fundamental groupoid as a $2$ -terminal costackhttps://projecteuclid.org/euclid.kjm/1571731342<strong>Ilia Pirashvili</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 25 pages.</p><p><strong>Abstract:</strong><br/>
We previously showed that the fundamental groupoid of a topological space can be defined by the Seifert–van Kampen theorem. This allowed us to give the first axiomatization of the topological fundamental groupoid. We will prove in this paper that the analogue holds for the étale fundamental groupoid of a Noetherian scheme $X$ as well.
</p>projecteuclid.org/euclid.kjm/1571731342_20200108040156Wed, 08 Jan 2020 04:01 ESTHomogeneous models for Levi degenerate CR manifoldshttps://projecteuclid.org/euclid.kjm/1570780814<strong>Andrea Santi</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 44 pages.</p><p><strong>Abstract:</strong><br/>
We extend the notion of a fundamental negatively $\mathbb{Z}$ -graded Lie algebra $\mathfrak{m}_{x}=\bigoplus _{p\leq -1}\mathfrak{m}_{x}^{p}$ associated to any point of a Levi nondegenerate Cauchy-Riemann (CR) manifold to the class of $k$ -nondegenerate CR manifolds $(M,\mathcal{D},\mathcal{J})$ for all $k\geq 2$ and call this invariant the core at $x\in M$ . It consists of a $\mathbb{Z}$ -graded vector space $\mathfrak{m}_{x}=\bigoplus _{p\leq k-2}\mathfrak{m}_{x}^{p}$ of height $k-2$ endowed with the natural algebraic structure induced by the Tanaka and Freeman sequences of $(M,\mathcal{D},\mathcal{J})$ and the Levi forms of higher order. In the case of CR manifolds of hypersurface type, we propose a definition of a homogeneous model of type $\mathfrak{m}$ , that is, a homogeneous $k$ -nondegenerate CR manifold $M=G/G_{o}$ with core $\mathfrak{m}$ associated with an appropriate $\mathbb{Z}$ -graded Lie algebra $\mathrm{Lie}(G)=\mathfrak{g}=\bigoplus \mathfrak{g}^{p}$ and subalgebra $\mathrm{Lie}(G_{o})=\mathfrak{g}_{o}=\bigoplus\mathfrak{g}_{o}^{p}$ of the nonnegative part $\bigoplus _{p\geq 0}\mathfrak{g}^{p}$ . It generalizes the classical notion of Tanaka of homogeneous models for Levi nondegenerate CR manifolds and the tube over the future light cone, the unique (up to local CR diffeomorphisms) maximally homogeneous $5$ -dimensional $2$ -nondegenerate CR manifold. We investigate the basic properties of cores and models and study the $7$ -dimensional CR manifolds of hypersurface type from this perspective. We first classify cores of $7$ -dimensional $2$ -nondegenerate CR manifolds up to isomorphism and then construct homogeneous models for seven of these classes. We finally show that there exists a unique core and homogeneous model in the $3$ -nondegenerate class.
</p>projecteuclid.org/euclid.kjm/1570780814_20200108040156Wed, 08 Jan 2020 04:01 ESTHausdorff operators on Morrey-type spaceshttps://projecteuclid.org/euclid.kjm/1568340110<strong>V. Burenkov</strong>, <strong>E. Liflyand</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 14 pages.</p><p><strong>Abstract:</strong><br/>
After 2000, interest in the Hausdorff operators grew, first in the sense of the variety of spaces on which these operators were considered. Here we give conditions ensuring the boundedness of such operators on Morrey-type spaces. The sharpness of the obtained results is studied, and classes of the Hausdorff operators are described for which the necessary and sufficient conditions coincide.
</p>projecteuclid.org/euclid.kjm/1568340110_20200108040156Wed, 08 Jan 2020 04:01 ESTToric Fano varieties associated to building setshttps://projecteuclid.org/euclid.kjm/1568102426<strong>Yusuke Suyama</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 15 pages.</p><p><strong>Abstract:</strong><br/>
We characterize building sets whose associated nonsingular projective toric varieties are Fano. Furthermore, we show that all such toric Fano varieties are obtained from smooth Fano polytopes associated to finite directed graphs.
</p>projecteuclid.org/euclid.kjm/1568102426_20200108040156Wed, 08 Jan 2020 04:01 ESTThree-dimensional purely quasimonomial actionshttps://projecteuclid.org/euclid.kjm/1578711622<strong>Akinari Hoshi</strong>, <strong>Hidetaka Kitayama</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 43 pages.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a finite subgroup of $\operatorname{Aut}_{k}(K(x_{1},\ldots ,x_{n}))$ , where $K/k$ is a finite field extension and $K(x_{1},\ldots,x_{n})$ is the rational function field with $n$ variables over $K$ . The action of $G$ on $K(x_{1},\ldots ,x_{n})$ is called quasimonomial if it satisfies the following three conditions: (i) $\sigma (K)\subset K$ for any $\sigma \in G$ ; (ii) $K^{G}=k$ , where $K^{G}$ is the fixed field under the action of $G$ ; (iii) for any $\sigma \in G$ and $1\leq j\leq n$ , $\sigma (x_{j})=c_{j}(\sigma )\prod _{i=1}^{n}x_{i}^{a_{ij}}$ , where $c_{j}(\sigma )\in K^{\times }$ and $[a_{i,j}]_{1\le i,j\le n}\in \operatorname{GL}_{n}(\mathbb{Z})$ . A quasimonomial action is called purely quasimonomial if $c_{j}(\sigma)=1$ for any $\sigma \in G$ and any $1\le j\le n$ . When $k=K$ , a quasimonomial action is called monomial . The main question is: Under what situations is $K(x_{1},\ldots ,x_{n})^{G}$ rational (i.e., $=$ purely transcendental) over $k$ ? For $n=1$ , the rationality problem was solved by Hoshi, Kang, and Kitayama. For $n=2$ , the problem was solved by Hajja when the action is monomial, by Voskresenskii when the action is faithful on $K$ and purely quasimonomial, which is equivalent to the rationality problem of $n$ -dimensional algebraic $k$ -tori which split over $K$ , and by Hoshi, Kang, and Kitayama when the action is purely quasimonomial. For $n=3$ , the problem was solved by Hajja, Kang, Hoshi, and Rikuna when the action is purely monomial, by Hoshi, Kitayama, and Yamasaki when the action is monomial except for one case, and by Kunyavskii when the action is faithful on $K$ and purely quasimonomial. In this paper, we determine the rationality when $n=3$ and the action is purely quasimonomial except for a few cases using a conjugacy classes move technique. As an application, we will show the rationality of some $5$ -dimensional purely monomial actions which are decomposable.
</p>projecteuclid.org/euclid.kjm/1578711622_20200110220041Fri, 10 Jan 2020 22:00 ESTCongruence primes for automorphic forms on unitary groups and applications to the arithmetic of Ikeda liftshttps://projecteuclid.org/euclid.kjm/1579230028<strong>Jim Brown</strong>, <strong>Krzysztof Klosin</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 39 pages.</p><p><strong>Abstract:</strong><br/>
In this paper we provide a sufficient condition for a prime to be a congruence prime for an automorphic form $f$ on the unitary group $\mathrm{U}(n,n)(\mathbf{A}_{F})$ for a large class of totally real fields $F$ via a divisibility of a special value of the standard $L$ -function associated to $f$ . We also study $\ell$ -adic properties of the Fourier coefficients of an Ikeda lift $I_{\phi}$ (of an elliptic modular form $\phi$ ) on $\mathrm{U}(n,n)(\mathbf{A}_{\mathbf{Q}})$ , proving that they are $\ell$ -adic integers which do not all vanish modulo $\ell$ . Finally we combine these results to show that the condition of $\ell$ being a congruence prime for $I_{\phi}$ is controlled by the $\ell$ -divisibility of a product of special values of the symmetric square $L$ -function of $\phi$ . We close the paper by computing an example when our main theorem applies.
</p>projecteuclid.org/euclid.kjm/1579230028_20200116220058Thu, 16 Jan 2020 22:00 ESTBoundedness of maximal operator for multilinear Calderón–Zygmund operators on products of variable Hardy spaceshttps://projecteuclid.org/euclid.kjm/1579748471<strong>Jian Tan</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 14 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we obtain boundedness of the maximal operator associated with multilinear Calderón–Zygmund singular integral operators from a product of variable Hardy spaces into variable Lebesgue spaces.
</p>projecteuclid.org/euclid.kjm/1579748471_20200122220133Wed, 22 Jan 2020 22:01 ESTPolynomial skew products whose Julia sets have infinitely many symmetrieshttps://projecteuclid.org/euclid.kjm/1579748472<strong>Kohei Ueno</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 21 pages.</p><p><strong>Abstract:</strong><br/>
We consider symmetries of Julia sets of polynomial skew products on $\mathbb{C}^{2}$ , which are birationally conjugate to rotational products. Our main result gives the classification of the polynomial skew products whose Julia sets have infinitely many symmetries.
</p>projecteuclid.org/euclid.kjm/1579748472_20200122220133Wed, 22 Jan 2020 22:01 ESTThe minimal regular model of a Fermat curve of odd squarefree exponent and its dualizing sheafhttps://projecteuclid.org/euclid.kjm/1580871614<strong>Christian Curilla</strong>, <strong>J. Steffen Müller</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 50 pages.</p><p><strong>Abstract:</strong><br/>
We construct the minimal regular model of the Fermat curve of odd squarefree composite exponent $N$ over the $N$ th cyclotomic integers. As an application, we compute upper and lower bounds for the arithmetic self-intersection of the dualizing sheaf of this model.
</p>projecteuclid.org/euclid.kjm/1580871614_20200204220049Tue, 04 Feb 2020 22:00 ESTRegular functions on spherical nilpotent orbits in complex symmetric pairs: Classical Hermitian caseshttps://projecteuclid.org/euclid.kjm/1581930017<strong>Paolo Bravi</strong>, <strong>Jacopo Gandini</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 60, Number 2, 405--450.</p><p><strong>Abstract:</strong><br/>
Given a classical semisimple complex algebraic group $G$ and a symmetric pair $(G,K)$ of Hermitian type, we study the closures of the spherical nilpotent $K$ -orbits in the isotropy representation of $K$ . We show that all such orbit closures are normal and describe the $K$ -module structure of their ring of regular functions.
</p>projecteuclid.org/euclid.kjm/1581930017_20200506220140Wed, 06 May 2020 22:01 EDTOn the $p$ -adic Birch and Swinnerton-Dyer conjecture for elliptic curves over number fieldshttps://projecteuclid.org/euclid.kjm/1582945269<strong>Daniel Disegni</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 60, Number 2, 473--510.</p><p><strong>Abstract:</strong><br/>
We formulate a multivariable $p$ -adic Birch and Swinnerton-Dyer conjecture for $p$ -ordinary elliptic curves $A$ over number fields $K$ . It generalizes the one-variable conjecture of Mazur, Tate, and Teitelbaum, who studied the case $K=\mathbf{Q}$ and the phenomenon of exceptional zeros. We discuss old and new theoretical evidence toward our conjecture and in particular we fully prove it, under mild conditions, in the following situation: $K$ is imaginary quadratic, $A=E_{K}$ is the base change to $K$ of an elliptic curve over the rationals, and the rank of $A$ is either 0 or $1$ .
The proof is naturally divided into a few cases. Some of them are deduced from the purely cyclotomic case of elliptic curves over $\mathbf{Q}$ , which we obtain from a refinement of recent work of Venerucci alongside the results of Greenberg, Stevens, Perrin-Riou, and the author. The only genuinely multivariable case (rank $1$ , two exceptional zeros, three partial derivatives) is newly established here. Its proof generalizes to show that the “almost-anticyclotomic” case of our conjecture is a consequence of conjectures of Bertolini and Darmon on families of Heegner points, and of (partly conjectural) $p$ -adic Gross–Zagier and Waldspurger formulas in families.
</p>projecteuclid.org/euclid.kjm/1582945269_20200506220140Wed, 06 May 2020 22:01 EDTDeformations of nonsingular Poisson varieties and Poisson invertible sheaveshttps://projecteuclid.org/euclid.kjm/1582340579<strong>Chunghoon Kim</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 60, Number 2, 511--541.</p><p><strong>Abstract:</strong><br/>
We study deformations of nonsingular Poisson varieties and Poisson invertible sheaves, which extend the flat deformation theory of nonsingular varieties and invertible sheaves. In the Appendix, we study deformations of Poisson vector bundles. We identify first-order deformations and obstructions.
</p>projecteuclid.org/euclid.kjm/1582340579_20200506220140Wed, 06 May 2020 22:01 EDT$C^{k}$ -regularity for $\bar{\partial }$ -equations for a class of convex domains of infinite type in $\mathbb{C}^{2}$https://projecteuclid.org/euclid.kjm/1582340578<strong>Ly Kim Ha</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 60, Number 2, 543--559.</p><p><strong>Abstract:</strong><br/>
The main purpose of this article is to study $C^{k}$ -regularity ( $k=0,1,\ldots $ ) for the Cauchy–Riemann equation \begin{equation*}\bar{\partial }u=\phi\end{equation*} on a smoothly bounded, convex domain of infinite type in $\mathbb{C}^{2}$ .
</p>projecteuclid.org/euclid.kjm/1582340578_20200506220140Wed, 06 May 2020 22:01 EDTEquivariant higher-index problems for proper actions and nonpositively curved manifoldshttps://projecteuclid.org/euclid.kjm/1582945268<strong>Xiaoman Chen</strong>, <strong>Benyin Fu</strong>, <strong>Qin Wang</strong>, <strong>Dapeng Zhou</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 60, Number 2, 575--591.</p><p><strong>Abstract:</strong><br/>
We prove that the equivariant higher-index map is injective for a bounded geometry metric space with a proper and isometric group action which can be equivariantly embedded into a simply connected, complete, and nonpositively curved Riemannian manifold with a proper and isometric group action.
</p>projecteuclid.org/euclid.kjm/1582945268_20200506220140Wed, 06 May 2020 22:01 EDTGrothendieck’s pairing on Néron component groups: Galois descent from the semistable casehttps://projecteuclid.org/euclid.kjm/1585792822<strong>Takashi Suzuki</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 60, Number 2, 593--716.</p><p><strong>Abstract:</strong><br/>
In our previous study of duality for complete discrete valuation fields with perfect residue field, we treated coefficients in finite flat group schemes. In this paper, we treat abelian varieties. This, in particular, implies Grothendieck’s conjecture on the perfectness of his pairing between the Néron component groups of an abelian variety and its dual. The point is that our formulation is well suited to Galois descent. From the known case of semistable abelian varieties, we deduce the perfectness in full generality. We also treat coefficients in tori and, more generally, $1$ -motives.
</p>projecteuclid.org/euclid.kjm/1585792822_20200506220140Wed, 06 May 2020 22:01 EDTThe second cohomology groups of nilpotent orbits in classical Lie algebrashttps://projecteuclid.org/euclid.kjm/1584064818<strong>Indranil Biswas</strong>, <strong>Pralay Chatterjee</strong>, <strong>Chandan Maity</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 60, Number 2, 717--799.</p><p><strong>Abstract:</strong><br/>
The second de Rham cohomology groups of nilpotent orbits in noncompact real forms of classical complex simple Lie algebras are explicitly computed. Furthermore, the first de Rham cohomology groups of nilpotent orbits in noncompact classical simple Lie algebras are computed, and we prove them to be zero for nilpotent orbits in all the complex simple Lie algebras. A key component in these computations is a description of the second and first cohomology groups of homogeneous spaces of general connected Lie groups which is obtained here. This description, which generalizes a previous theorem of the first two authors, may be of independent interest.
</p>projecteuclid.org/euclid.kjm/1584064818_20200506220140Wed, 06 May 2020 22:01 EDT