Registered users receive a variety of benefits including the ability to customize email alerts, create favorite journals list, and save searches.
Please note that a Project Euclid web account does not automatically grant access to full-text content. An institutional or society member subscription is required to view non-Open Access content.
Contact firstname.lastname@example.org with any questions.
We construct a minimal projective bimodule resolution for every finite-dimensional quantum complete intersection of codimension two. Then we use this resolution to compute both the Hochschild cohomology and homology for such an algebra. In particular, we show that the cohomology vanishes in high degrees, while the homology is always nonzero.
We give an explicit description of the terms and differentials of the Tate resolution of sheaves arising from Segre embeddings of . We prove that the maps in this Tate resolution are either coming from Sylvester-type maps, or from Bezout-type maps arising from the so-called toric Jacobian.
For any finite graph and any field of characteristic unequal to , we construct an algebraic variety over whose -points parametrize -Lie algebras generated by extremal elements, corresponding to the vertices of the graph, with prescribed commutation relations, corresponding to the nonedges. After that, we study the case where is a connected, simply laced Dynkin diagram of finite or affine type. We prove that is then an affine space, and that all points in an open dense subset of parametrize Lie algebras isomorphic to a single fixed Lie algebra. If is of affine type, then this fixed Lie algebra is the split finite-dimensional simple Lie algebra corresponding to the associated finite-type Dynkin diagram. This gives a new construction of these Lie algebras, in which they come together with interesting degenerations, corresponding to points outside the open dense subset. Our results may prove useful for recognizing these Lie algebras.
We define traces associated to a weakly holomorphic modular form of arbitrary negative even integral weight and show that these traces appear as coefficients of certain weakly holomorphic forms of half-integral weight. If the coefficients of are integral, then these traces are integral as well. We obtain a negative weight analogue of the classical Shintani lift and give an application to a generalization of the Shimura lift.
On établit une suite exacte décrivant l’adhérence des points rationnels d’un -motif dans ses points adéliques. On en déduit ensuite que le défaut d’approximation forte pour un groupe algébrique commutatif est essentiellement mesuré par son groupe de Brauer algébrique via l’obstruction de Brauer-Manin entière.
We give an exact sequence describing the closure of the set of rational points of a -motive in its adelic points. From this we deduce that for a commutative algebraic group, the defect of strong approximation is essentially controlled by its algebraic Brauer group, by means of the integral Brauer-Manin obstruction.