@article{ASENS_2005_4_38_4_505_0, author = {Dimitrov, Mladen}, title = {Galois representations modulo $p$ and cohomology of {Hilbert} modular varieties}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {505--551}, publisher = {Elsevier}, volume = {Ser. 4, 38}, number = {4}, year = {2005}, doi = {10.1016/j.ansens.2005.03.005}, zbl = {02231414}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.ansens.2005.03.005/} }
TY - JOUR AU - Dimitrov, Mladen TI - Galois representations modulo $p$ and cohomology of Hilbert modular varieties JO - Annales scientifiques de l'École Normale Supérieure PY - 2005 SP - 505 EP - 551 VL - 38 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.ansens.2005.03.005/ DO - 10.1016/j.ansens.2005.03.005 LA - en ID - ASENS_2005_4_38_4_505_0 ER -
%0 Journal Article %A Dimitrov, Mladen %T Galois representations modulo $p$ and cohomology of Hilbert modular varieties %J Annales scientifiques de l'École Normale Supérieure %D 2005 %P 505-551 %V 38 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.ansens.2005.03.005/ %R 10.1016/j.ansens.2005.03.005 %G en %F ASENS_2005_4_38_4_505_0
Dimitrov, Mladen. Galois representations modulo $p$ and cohomology of Hilbert modular varieties. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 38 (2005) no. 4, pp. 505-551. doi : 10.1016/j.ansens.2005.03.005. http://archive.numdam.org/articles/10.1016/j.ansens.2005.03.005/
[1] Motives for Hilbert modular forms, Invent. Math. 114 (1993) 55-87. | MR | Zbl
, ,[2] Une remarque sur les représentations locales p-adiques et les congruences entre formes modulaires de Hilbert, Bull. Soc. Math. France 127 (1999) 459-472. | Numdam | MR | Zbl
,[3] Cohomologie d'intersection et fonctions L de certaines variétés de Shimura, Ann. Sci. École Norm. Sup. 17 (1984) 361-412. | Numdam | MR | Zbl
, ,[4] Formes modulaires et représentations l-adiques, in: Séminaire Bourbaki, 355, Lecture Notes in Math., vol. 179, Springer, Berlin, 1971. | Numdam | Zbl
,[5] La conjecture de Weil. I, Publ. Math. IHÉS 43 (1974) 273-307. | Numdam | MR | Zbl
,[6] Valeurs de fonctions L et périodes d'intégrales, in: Proceedings of Symposia of Pure Mathematics, vol. 33, American Mathematical Society, Providence, RI, 1979, pp. 313-346. | MR | Zbl
,[7] Formes modulaires de poids 1, Ann. Sci. École Norm. Sup. 7 (1974) 507-530. | Numdam | MR | Zbl
, ,[8] On the Hecke action on the cohomology of Hilbert-Blumenthal surfaces, Contemp. Math. 210 (1998) 71-83. | MR | Zbl
,[9] The Tamagawa number conjecture of adjoint motives of modular forms, Ann. Sci. École Norm. Sup. 37 (2004) 663-727. | Numdam | MR | Zbl
, , ,[10] Compactifications arithmétiques des variétés de Hilbert et formes modulaires de Hilbert pour , in: , , , , (Eds.), Geometric Aspects of Dwork Theory, Walter de Gruyter, Berlin, 2004, pp. 527-554. | MR | Zbl
,[11] Variétés et formes modulaires de Hilbert arithmétiques pour , in: , , , , (Eds.), Geometric Aspects of Dwork Theory, Walter de Gruyter, Berlin, 2004, pp. 555-614. | MR | Zbl
, ,[12] On Ihara's lemma for Hilbert modular varieties, math.NT/0503134.
,[13] On the cohomology of locally symmetric Hermitian spaces, in: Séminaire d'algèbre, Lecture Notes in Math., vol. 1029, Springer, Berlin, 1983, pp. 349-366. | MR | Zbl
,[14] Crystalline cohomology and p-adic Galois representations, in: (Ed.), Algebraic Analysis, Geometry, and Number Theory, 1989, pp. 25-80. | MR | Zbl
,[15] Degeneration of Abelian Varieties, Springer, Berlin, 1990. | MR | Zbl
, ,[16] Crystalline cohomology and , Israel J. Math. 90 (1995) 1-66. | MR | Zbl
, ,[17] Construction de représentations p-adiques, Ann. Sci. École Norm. Sup. 15 (1982) 547-608. | Numdam | MR | Zbl
, ,[18] Adjoint L-values and primes of congruence for Hilbert modular forms, Compositio Math. 132 (2002) 243-281. | MR | Zbl
,[19] Eisenstein cohomology of arithmetic groups. The case , Invent. Math. 89 (1987) 37-118. | MR | Zbl
,[20] p-adic Automorphic Forms on Shimura Varieties, Springer, Berlin, 2004. | MR | Zbl
,[21] Congruences of cusp forms and special values of their zeta functions, Invent. Math. 63 (1981) 225-261. | MR | Zbl
,[22] On congruence divisors of cuspforms as factors of the special values of their zeta functions, Invent. Math. 64 (1981) 221-262. | MR | Zbl
,[23] Nearly ordinary Hecke algebras and Galois representations of several variables, in: Algebraic Analysis, Geometry and Number Theory, Proceedings of the JAMI Inaugural Conference, 1988, pp. 115-134. | MR | Zbl
,[24] On p-adic Hecke algebras for over totally real fields, Ann. of Math. 128 (1988) 295-384. | MR | Zbl
,[25] On the critical values of L-functions of and , Duke Math. J. 74 (1994) 431-529. | MR | Zbl
,[26] Anti-cyclotomic Katz p-adic L-functions and congruence modules, Ann. Sci. École Norm. Sup. 26 (1993) 189-259. | Numdam | MR | Zbl
, ,[27] Réduction semi-stable et décomposition de complexes de de Rham à coefficients, Duke Math. J. 60 (1990) 139-185. | MR | Zbl
,[28] Representations of Algebraic Groups, Academic Press, New York, 1987. | MR | Zbl
,[29] M. Kisin, K. Lai, Overconvergent Hilbert modular forms, Amer. J. Math., submitted for publication. | MR | Zbl
[30] Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. 47 (1977) 33-186. | Numdam | MR | Zbl
,[31] Cohomology of Siegel varieties with p-adic integral coefficients and applications, in: Cohomology of Siegel Varieties, Astérisque, vol. 280, 2002, pp. 1-95. | Numdam | MR | Zbl
, ,[32] On l-adic sheaves on Shimura varieties and their higher images in the Baily-Borel compactification, Math. Ann. 292 (1992) 197-240. | MR | Zbl
,[33] Bernstein-Gelfand-Gelfand complexes and cohomology of nilpotent groups over for representations with p-small weights, in: Cohomology of Siegel Varieties, Astérisque, vol. 280, 2002, pp. 97-135. | Numdam | MR | Zbl
, ,[34] Compactification de l'espace de modules de Hilbert-Blumenthal, Compositio Math. 36 (1978) 255-335. | Numdam | MR | Zbl
,[35] On l-adic representations attached to modular forms, Invent. Math. 28 (1975) 245-275. | MR | Zbl
,[36] Mod p Hecke operators and congruences between modular forms, Invent. Math. 71 (1983) 193-205. | MR | Zbl
,[37] Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math. 15 (1972) 259-331. | MR | Zbl
,[38] The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J. 45 (1978) 637-679. | MR | Zbl
,[39] Representations of algebraic groups, Nagoya Math. J. 22 (1963) 33-56. | MR | Zbl
,[40] On Galois representations associated to Hilbert modular forms, Invent. Math. 98 (1989) 265-280. | MR | Zbl
,[41] On Galois representations associated to Hilbert modular forms II, in: , (Eds.), Elliptic Curves, Modular Forms and Fermat's Last Theorem, Hong Kong, 1993, International Press, 1995, pp. 185-191. | MR | Zbl
,[42] Congruence relations on some Shimura varieties, J. reine angew. Math. 524 (2000) 43-71. | MR | Zbl
,[43] On ordinary λ-adic representations associated to modular forms, Invent. Math. 94 (1988) 529-573. | Zbl
,[44] On the zeta functions of Shimura varieties and periods of Hilbert modular forms, Duke Math. J. 74 (1994) 121-191. | MR | Zbl
,Cited by Sources: