Module de congruences pour $\mathrm{GL}(2)$ d’un corps imaginaire quadratique et théorie d’Iwasawa d’un corps CM biquadratique

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Module de congruences pour $\mathrm{GL}(2)$ d’un corps imaginaire quadratique et théorie d’Iwasawa d’un corps CM biquadratique

Eric Urban

Source: Duke Math. J. Volume 92, Number 1 (1998), 179-220.

First Page: Show

Primary Subjects: 11F33

Secondary Subjects: 11F75, 11F80, 11R23

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077231297
Mathematical Reviews number (MathSciNet): MR1611003
Zentralblatt MATH identifier: 0973.11095
Digital Object Identifier: doi:10.1215/S0012-7094-98-09204-3

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References

[BR] D. Blasius and D. Ramakrishnan, Maass forms and Galois representations, Galois groups over $\bf Q$ (Berkeley, CA, 1987), Math. Sci. Res. Inst. Publ., vol. 16, Springer-Verlag, New York, 1989, pp. 33–77.

Mathematical Reviews (MathSciNet): MR90m:11078

Zentralblatt MATH: 0699.10043

[Bo] A. Borel, Automorphic $L$-functions, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc., Providence, R.I., 1979, pp. 27–61.

Mathematical Reviews (MathSciNet): MR81m:10056

Zentralblatt MATH: 0412.10017

[BS] A. Borel and J.-P. Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973), 436–491.

Mathematical Reviews (MathSciNet): MR52:8337

Zentralblatt MATH: 0274.22011

Digital Object Identifier: doi:10.1007/BF02566134

[Br] G. E. Bredon, Sheaf Theory, McGraw-Hill Book Co., New York, 1967.

Mathematical Reviews (MathSciNet): MR36:4552

Zentralblatt MATH: 0158.20505

[Ca] H. Carayol, Formes modulaires et représentations galoisiennes à valeurs dans un anneau local complet, $p$-adic monodromy and the Birch and Swinnerton-Dyer conjecture (Boston, MA, 1991), Contemp. Math., vol. 165, Amer. Math. Soc., Providence, RI, 1994, pp. 213–237.

Mathematical Reviews (MathSciNet): MR95i:11059

Zentralblatt MATH: 0812.11036

[C] W. Casselman, On some results of Atkin and Lehner, Math. Ann. 201 (1973), 301–314.

Mathematical Reviews (MathSciNet): MR49:2558

Zentralblatt MATH: 0239.10015

Digital Object Identifier: doi:10.1007/BF01428197

[CR] C. W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Pure and Applied Mathematics, vol. 11, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1962.

Mathematical Reviews (MathSciNet): MR26:2519

Zentralblatt MATH: 0131.25601

[FH] S. Friedberg and J. Hoffstein, Nonvanishing theorems for automorphic $L$-functions on $\rm GL(2)$, Ann. of Math. (2) 142 (1995), no. 2, 385–423.

Mathematical Reviews (MathSciNet): MR96e:11072

Zentralblatt MATH: 0847.11026

Digital Object Identifier: doi:10.2307/2118638

JSTOR: links.jstor.org

[G] S. Gelbart, Automorphic forms on adèle groups, Ann. of Math. Stud., vol. 83, Princeton University Press, Princeton, N.J., 1975.

Mathematical Reviews (MathSciNet): MR52:280

Zentralblatt MATH: 0329.10018

[Gr] R. Greenberg, Iwasawa theory and $p$-adic deformations of motives, Motives (Seattle, WA, 1991),II, Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 193–223.

Mathematical Reviews (MathSciNet): MR95i:11053

Zentralblatt MATH: 0819.11046

[Ha] G. Harder, Eisenstein cohomology of arithmetic groups. The case $\rm GL\sb 2$, Invent. Math. 89 (1987), no. 1, 37–118.

Mathematical Reviews (MathSciNet): MR89b:22018

Zentralblatt MATH: 0629.10023

Digital Object Identifier: doi:10.1007/BF01404673

[HST] M. Harris, D. Soudry, and R. Taylor, $l$-adic representations associated to modular forms over imaginary quadratic fields. I. Lifting to $\rm GSp\sb 4(\bf Q)$, Invent. Math. 112 (1993), no. 2, 377–411.

Mathematical Reviews (MathSciNet): MR94d:11035

Zentralblatt MATH: 0797.11047

Digital Object Identifier: doi:10.1007/BF01232440

[Hi1] H. Hida, A $p$-adic measure attached to the zeta functions associated with two elliptic modular forms. I, Invent. Math. 79 (1985), no. 1, 159–195.

Mathematical Reviews (MathSciNet): MR86m:11097

Zentralblatt MATH: 0573.10020

Digital Object Identifier: doi:10.1007/BF01388661

[Hi2] H. Hida, $p$-ordinary cohomology groups for $\rm SL(2)$ over number fields, Duke Math. J. 69 (1993), no. 2, 259–314.

Mathematical Reviews (MathSciNet): MR94g:11031

Zentralblatt MATH: 0941.11024

Digital Object Identifier: doi:10.1215/S0012-7094-93-06914-1

Project Euclid: euclid.dmj/1077293571

[Hi3] H. Hida, On the critical values of $L$-functions of $\rm GL(2)$ and $\rm GL(2)\times\rm GL(2)$, Duke Math. J. 74 (1994), no. 2, 431–529.

Mathematical Reviews (MathSciNet): MR98f:11043

Zentralblatt MATH: 0838.11036

Digital Object Identifier: doi:10.1215/S0012-7094-94-07417-6

Project Euclid: euclid.dmj/1077288205

[Hi4] H. Hida, On $p$-adic Hecke algebras for $\rm GL\sb 2$ over totally real fields, Ann. of Math. (2) 128 (1988), no. 2, 295–384.

Mathematical Reviews (MathSciNet): MR89m:11046

Zentralblatt MATH: 0658.10034

Digital Object Identifier: doi:10.2307/1971444

JSTOR: links.jstor.org

[Hi5] H. Hida, Control theorems of $p$-nearly ordinary cohomology groups for $\rm SL(n)$, Bull. Soc. Math. France 123 (1995), no. 3, 425–475.

Mathematical Reviews (MathSciNet): MR97c:11053

Zentralblatt MATH: 0852.11023

[Hi6] H. Hida, $p$-adic ordinary Hecke algebras for $\rm GL(2)$, Ann. Inst. Fourier (Grenoble) 44 (1994), no. 5, 1289–1322.

Mathematical Reviews (MathSciNet): MR95k:11065

Zentralblatt MATH: 0819.11017

[Hi7] H. Hida, Hecke algebras for $\rm GL\sb 1$ and $\rm GL\sb 2$, Séminaire de théorie des nombres, Paris 1984–85, Progr. Math., vol. 63, Birkhäuser Boston, Boston, MA, 1986, pp. 131–163.

Mathematical Reviews (MathSciNet): MR88i:11078

Zentralblatt MATH: 0648.10020

[HT1] H. Hida and J. Tilouine, Katz $p$-adic $L$-functions, congruence modules and deformation of Galois representations, $L$-functions and arithmetic (Durham, 1989), London Math. Soc. Lecture Note Ser., vol. 153, Cambridge Univ. Press, Cambridge, 1991, pp. 271–293.

Mathematical Reviews (MathSciNet): MR93c:11027

Zentralblatt MATH: 0739.11022

Digital Object Identifier: doi:10.1017/CBO9780511526053.011

[HT2] H. Hida and J. Tilouine, On the anticyclotomic main conjecture for CM fields, Invent. Math. 117 (1994), no. 1, 89–147.

Mathematical Reviews (MathSciNet): MR95d:11149

Zentralblatt MATH: 0819.11047

Digital Object Identifier: doi:10.1007/BF01232236

[JL] H. Jacquet and R. Langlands, Automorphic forms on $\rm GL(2)$, Lecture notes in Math., vol. 114, Springer-Verlag, Berlin, 1970.

Mathematical Reviews (MathSciNet): MR53:5481

Zentralblatt MATH: 0236.12010

[K] N. Katz, $p$-adic $L$-functions for CM fields, Invent. Math. 49 (1978), no. 3, 199–297.

Mathematical Reviews (MathSciNet): MR80h:10039

Zentralblatt MATH: 0417.12003

Digital Object Identifier: doi:10.1007/BF01390187

[L] R. Langlands, Modular forms and $\ell$-adic representations, Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Lecture Notes in Math., vol. 349, Springer, Berlin, 1973, pp. 361–500.

Mathematical Reviews (MathSciNet): MR50:7095

Zentralblatt MATH: 0279.14007

[MT] B. Mazur and J. Tilouine, Représentations galoisiennes, différentielles de Kähler et “conjectures principales”, Inst. Hautes Études Sci. Publ. Math. (1990), no. 71, 65–103.

Mathematical Reviews (MathSciNet): MR92e:11060

Zentralblatt MATH: 0744.11053

Digital Object Identifier: doi:10.1007/BF02699878

[M] T. Miyake, On automorphic forms on $\rm GL\sb2$ and Hecke operators, Ann. of Math. (2) 94 (1971), 174–189.

Mathematical Reviews (MathSciNet): MR45:8607

Zentralblatt MATH: 0215.37301

Digital Object Identifier: doi:10.2307/1970741

JSTOR: links.jstor.org

[Ny] L. Nyssen, Pseudo-représentations, Math. Ann. 306 (1996), no. 2, 257–283.

Mathematical Reviews (MathSciNet): MR98a:20013

Zentralblatt MATH: 0863.16012

Digital Object Identifier: doi:10.1007/BF01445251

[P] B. Perrin-Riou, Groupe de Selmer d'une courbe elliptique à multiplication complexe, Compositio Math. 43 (1981), no. 3, 387–417.

Mathematical Reviews (MathSciNet): MR83i:14031

Zentralblatt MATH: 0479.14019

[P2] B. Perrin-Riou, Représentations $p$-adiques ordinaires, Astérisque (1994), no. 223, 185–220, dans Périods $p$-adiques (Bures-sur-Yvette, 1988), Soc. Math. France, Montrouge.

Mathematical Reviews (MathSciNet): MR96h:11063

Zentralblatt MATH: 00732150

[R] D. Ramakrishnan, A refinement of the strong multiplicity one theorem for $\rm GL(2)$. Appendix to: “$l$-adic representations associated to modular forms over imaginary quadratic fields. II”, Invent. Math. 116 (1994), no. 1-3, 645–649.

Mathematical Reviews (MathSciNet): MR95h:11050b

Zentralblatt MATH: 0823.11021

Digital Object Identifier: doi:10.1007/BF01231576

[S] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo, Princeton Univ., Princeton, 1971.

Mathematical Reviews (MathSciNet): MR47:3318

Zentralblatt MATH: 0221.10029

[Tay1] R. Taylor, Congruences between modular forms for $\mathrmGL(2)$ over an imaginary quadratic field, Ph.D. thesis, Cambridge Univ., 1987.

[Tay2] R. Taylor, $l$-adic representations associated to modular forms over imaginary quadratic fields. II, Invent. Math. 116 (1994), no. 1-3, 619–643.

Mathematical Reviews (MathSciNet): MR95h:11050a

Zentralblatt MATH: 0823.11020

Digital Object Identifier: doi:10.1007/BF01231575

[Tay3] R. Taylor, Galois representations associated to Siegel modular forms of low weight, Duke Math. J. 63 (1991), no. 2, 281–332.

Mathematical Reviews (MathSciNet): MR92j:11044

Zentralblatt MATH: 0810.11033

Digital Object Identifier: doi:10.1215/S0012-7094-91-06312-X

Project Euclid: euclid.dmj/1077295922

[Tay4] R. Taylor, On the $l$-adic cohomology of Siegel threefolds, Invent. Math. 114 (1993), no. 2, 289–310.

Mathematical Reviews (MathSciNet): MR95j:11054

Zentralblatt MATH: 0810.11034

Digital Object Identifier: doi:10.1007/BF01232672

[Ti1] J. Tilouine, Théorie d'Iwasawa classique et de l'algèbre de Hecke ordinaire, Compositio Math. 65 (1988), no. 3, 265–320.

Mathematical Reviews (MathSciNet): MR89f:11152

Zentralblatt MATH: 0663.12008

[Ti2] J. Tilouine, Déformations of Galois representations and Hecke algebras, Published for The Mehta Research Institute of Mathematics and Mathematical Physics, Allahabad, 1996.

Mathematical Reviews (MathSciNet): MR99i:11038

Zentralblatt MATH: 1009.11033

[Ti3] J. Tilouine, Kümmer's criterion over $\Lambda$, Hokkaïdo Univ. Tech. Rep. Ser. Math. (1987), no. 4.

[TU1] J. Tilouine and E. Urban, Familles $p$-adiques à trois variables de formes de Siegel et de représentations galoisiennes, C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), no. 1, 5–10.

Mathematical Reviews (MathSciNet): MR96c:11048

Zentralblatt MATH: 00837095

[TU2] J. Tilouine and E. Urban, Several variable $p$-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations, prepublication 97-04, Univ. Paris-Nord, 1997.

[U1] E. Urban, Formes automorphes cuspidales pour $\rm GL\sb 2$ sur un corps quadratique imaginaire. Valeurs spéciales de fonctions $L$ et congruences, Compositio Math. 99 (1995), no. 3, 283–324.

Mathematical Reviews (MathSciNet): MR96m:11039

Zentralblatt MATH: 0846.11029

[U2] E. Urban, Arithmétique des formes modulaires pour $\mathrmGL_2$ sur un corps imaginaire quadratique, thèse, Univ. d'Orsay, 1994, 283–324.

[W1] A. Weil, Dirichlet Series and Automorphic Forms, Lecture Notes in Math., vol. 189, Springer-Verlag, Berlin, 1971.

Zentralblatt MATH: 0218.10046

[W2] A. Weil, On a certain type of characters of the idèle-class group of an algebraic number field, Ocurres Scientifique: Collected Papers, Vol. 2, Springer-Verlag, New York, 1979, pp. 255–261.

[We] R. Weissauer, A special case of the fundamental lemma: The case of $Sp_4(F)$, prepublication.

[Wi] A. Wiles, On ordinary $\lambda$-adic representations associated to modular forms, Invent. Math. 94 (1988), no. 3, 529–573.

Mathematical Reviews (MathSciNet): MR89j:11051

Zentralblatt MATH: 0664.10013

Digital Object Identifier: doi:10.1007/BF01394275

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