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.
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     author = {Dimitrov, Mladen},
     title = {Galois representations modulo $p$ and cohomology of {Hilbert} modular varieties},
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     url = {http://archive.numdam.org/articles/10.1016/j.ansens.2005.03.005/}
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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] Blasius D., Rogawski J., Motives for Hilbert modular forms, Invent. Math. 114 (1993) 55-87. | MR | Zbl

[2] Breuil C., 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] Brylinski J.-L., Labesse J.-P., Cohomologie d'intersection et fonctions L de certaines variétés de Shimura, Ann. Sci. École Norm. Sup. 17 (1984) 361-412. | Numdam | MR | Zbl

[4] Deligne P., Formes modulaires et représentations l-adiques, in: Séminaire Bourbaki, 355, Lecture Notes in Math., vol. 179, Springer, Berlin, 1971. | Numdam | Zbl

[5] Deligne P., La conjecture de Weil. I, Publ. Math. IHÉS 43 (1974) 273-307. | Numdam | MR | Zbl

[6] Deligne P., 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] Deligne P., Serre J.-P., Formes modulaires de poids 1, Ann. Sci. École Norm. Sup. 7 (1974) 507-530. | Numdam | MR | Zbl

[8] Diamond F., On the Hecke action on the cohomology of Hilbert-Blumenthal surfaces, Contemp. Math. 210 (1998) 71-83. | MR | Zbl

[9] Diamond F., Flach M., Guo L., The Tamagawa number conjecture of adjoint motives of modular forms, Ann. Sci. École Norm. Sup. 37 (2004) 663-727. | Numdam | MR | Zbl

[10] Dimitrov M., Compactifications arithmétiques des variétés de Hilbert et formes modulaires de Hilbert pour Γ 1 (c,n), in: Adolphson A., Baldassarri F., Berthelot P., Katz N., Loeser F. (Eds.), Geometric Aspects of Dwork Theory, Walter de Gruyter, Berlin, 2004, pp. 527-554. | MR | Zbl

[11] Dimitrov M., Tilouine J., Variétés et formes modulaires de Hilbert arithmétiques pour Γ 1 (c,n), in: Adolphson A., Baldassarri F., Berthelot P., Katz N., Loeser F. (Eds.), Geometric Aspects of Dwork Theory, Walter de Gruyter, Berlin, 2004, pp. 555-614. | MR | Zbl

[12] Dimitrov M., On Ihara's lemma for Hilbert modular varieties, math.NT/0503134.

[13] Faltings G., 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] Faltings G., Crystalline cohomology and p-adic Galois representations, in: Press J.H.U. (Ed.), Algebraic Analysis, Geometry, and Number Theory, 1989, pp. 25-80. | MR | Zbl

[15] Faltings G., Chai C.-L., Degeneration of Abelian Varieties, Springer, Berlin, 1990. | MR | Zbl

[16] Faltings G., Jordan B., Crystalline cohomology and GL (2,Q), Israel J. Math. 90 (1995) 1-66. | MR | Zbl

[17] Fontaine J.-M., Laffaille G., Construction de représentations p-adiques, Ann. Sci. École Norm. Sup. 15 (1982) 547-608. | Numdam | MR | Zbl

[18] Ghate E., Adjoint L-values and primes of congruence for Hilbert modular forms, Compositio Math. 132 (2002) 243-281. | MR | Zbl

[19] Harder G., Eisenstein cohomology of arithmetic groups. The case GL 2 , Invent. Math. 89 (1987) 37-118. | MR | Zbl

[20] Hida H., p-adic Automorphic Forms on Shimura Varieties, Springer, Berlin, 2004. | MR | Zbl

[21] Hida H., Congruences of cusp forms and special values of their zeta functions, Invent. Math. 63 (1981) 225-261. | MR | Zbl

[22] Hida H., On congruence divisors of cuspforms as factors of the special values of their zeta functions, Invent. Math. 64 (1981) 221-262. | MR | Zbl

[23] Hida H., 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] Hida H., On p-adic Hecke algebras for GL 2 over totally real fields, Ann. of Math. 128 (1988) 295-384. | MR | Zbl

[25] Hida H., On the critical values of L-functions of GL 2 and GL 2 × GL 2 , Duke Math. J. 74 (1994) 431-529. | MR | Zbl

[26] Hida H., Tilouine J., Anti-cyclotomic Katz p-adic L-functions and congruence modules, Ann. Sci. École Norm. Sup. 26 (1993) 189-259. | Numdam | MR | Zbl

[27] Illusie L., Réduction semi-stable et décomposition de complexes de de Rham à coefficients, Duke Math. J. 60 (1990) 139-185. | MR | Zbl

[28] Jantzen J., 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] Mazur B., Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. 47 (1977) 33-186. | Numdam | MR | Zbl

[31] Mokrane A., Tilouine J., Cohomology of Siegel varieties with p-adic integral coefficients and applications, in: Cohomology of Siegel Varieties, Astérisque, vol. 280, 2002, pp. 1-95. | MR | Zbl

[32] Pink R., 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] Polo P., Tilouine J., Bernstein-Gelfand-Gelfand complexes and cohomology of nilpotent groups over Z p for representations with p-small weights, in: Cohomology of Siegel Varieties, Astérisque, vol. 280, 2002, pp. 97-135. | MR | Zbl

[34] Rapoport M., Compactification de l'espace de modules de Hilbert-Blumenthal, Compositio Math. 36 (1978) 255-335. | Numdam | MR | Zbl

[35] Ribet K., On l-adic representations attached to modular forms, Invent. Math. 28 (1975) 245-275. | MR | Zbl

[36] Ribet K., Mod p Hecke operators and congruences between modular forms, Invent. Math. 71 (1983) 193-205. | MR | Zbl

[37] Serre J.-P., Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math. 15 (1972) 259-331. | MR | Zbl

[38] Shimura G., The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J. 45 (1978) 637-679. | MR | Zbl

[39] Steinberg R., Representations of algebraic groups, Nagoya Math. J. 22 (1963) 33-56. | MR | Zbl

[40] Taylor R., On Galois representations associated to Hilbert modular forms, Invent. Math. 98 (1989) 265-280. | MR | Zbl

[41] Taylor R., On Galois representations associated to Hilbert modular forms II, in: Coates J., Yau S.-T. (Eds.), Elliptic Curves, Modular Forms and Fermat's Last Theorem, Hong Kong, 1993, International Press, 1995, pp. 185-191. | MR | Zbl

[42] Wedhorn T., Congruence relations on some Shimura varieties, J. reine angew. Math. 524 (2000) 43-71. | MR | Zbl

[43] Wiles A., On ordinary λ-adic representations associated to modular forms, Invent. Math. 94 (1988) 529-573. | Zbl

[44] Yoshida H., On the zeta functions of Shimura varieties and periods of Hilbert modular forms, Duke Math. J. 74 (1994) 121-191. | MR | Zbl

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