Galois representations modulo p and cohomology of Hilbert modular varieties
Annales scientifiques de l'École Normale Supérieure (2005)
- Volume: 38, Issue: 4, page 505-551
- ISSN: 0012-9593
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topDimitrov, Mladen. "Galois representations modulo p and cohomology of Hilbert modular varieties." Annales scientifiques de l'École Normale Supérieure 38.4 (2005): 505-551. <http://eudml.org/doc/82667>.
@article{Dimitrov2005,
author = {Dimitrov, Mladen},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {4},
pages = {505-551},
publisher = {Elsevier},
title = {Galois representations modulo p and cohomology of Hilbert modular varieties},
url = {http://eudml.org/doc/82667},
volume = {38},
year = {2005},
}
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
PB - Elsevier
VL - 38
IS - 4
SP - 505
EP - 551
LA - eng
UR - http://eudml.org/doc/82667
ER -
References
top- [1] Blasius D., Rogawski J., Motives for Hilbert modular forms, Invent. Math.114 (1993) 55-87. Zbl0829.11028MR1235020
- [2] Breuil C., Une remarque sur les représentations locales p-adiques et les congruences entre formes modulaires de Hilbert, Bull. Soc. Math. France127 (1999) 459-472. Zbl0933.11028MR1724405
- [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. Zbl0553.12005MR777375
- [4] Deligne P., Formes modulaires et représentations l-adiques, in: Séminaire Bourbaki, 355, Lecture Notes in Math., vol. 179, Springer, Berlin, 1971. Zbl0206.49901
- [5] Deligne P., La conjecture de Weil. I, Publ. Math. IHÉS43 (1974) 273-307. Zbl0287.14001MR340258
- [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. Zbl0449.10022MR546622
- [7] Deligne P., Serre J.-P., Formes modulaires de poids 1, Ann. Sci. École Norm. Sup.7 (1974) 507-530. Zbl0321.10026MR379379
- [8] Diamond F., On the Hecke action on the cohomology of Hilbert–Blumenthal surfaces, Contemp. Math.210 (1998) 71-83. Zbl0923.11074MR1478485
- [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. Zbl1121.11045MR2103471
- [10] Dimitrov M., Compactifications arithmétiques des variétés de Hilbert et formes modulaires de Hilbert pour , 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. Zbl1076.14029MR2099078
- [11] Dimitrov M., Tilouine J., Variétés et formes modulaires de Hilbert arithmétiques pour , 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. Zbl1127.11036MR2099080
- [12] Dimitrov M., On Ihara's lemma for Hilbert modular varieties, math.NT/0503134. Zbl1256.11035
- [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. Zbl0539.22008MR732471
- [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. Zbl0805.14008MR1463696
- [15] Faltings G., Chai C.-L., Degeneration of Abelian Varieties, Springer, Berlin, 1990. Zbl0744.14031MR1083353
- [16] Faltings G., Jordan B., Crystalline cohomology and , Israel J. Math.90 (1995) 1-66. Zbl0854.14010MR1336315
- [17] Fontaine J.-M., Laffaille G., Construction de représentations p-adiques, Ann. Sci. École Norm. Sup.15 (1982) 547-608. Zbl0579.14037MR707328
- [18] Ghate E., Adjoint L-values and primes of congruence for Hilbert modular forms, Compositio Math.132 (2002) 243-281. Zbl1004.11019MR1918132
- [19] Harder G., Eisenstein cohomology of arithmetic groups. The case , Invent. Math.89 (1987) 37-118. Zbl0629.10023MR892187
- [20] Hida H., p-adic Automorphic Forms on Shimura Varieties, Springer, Berlin, 2004. Zbl1055.11032MR2055355
- [21] Hida H., Congruences of cusp forms and special values of their zeta functions, Invent. Math.63 (1981) 225-261. Zbl0459.10018MR610538
- [22] Hida H., On congruence divisors of cuspforms as factors of the special values of their zeta functions, Invent. Math.64 (1981) 221-262. Zbl0472.10028MR629471
- [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. Zbl0782.11017MR1463699
- [24] Hida H., On p-adic Hecke algebras for over totally real fields, Ann. of Math.128 (1988) 295-384. Zbl0658.10034MR960949
- [25] Hida H., On the critical values of L-functions of and , Duke Math. J.74 (1994) 431-529. Zbl0838.11036MR1272981
- [26] Hida H., Tilouine J., Anti-cyclotomic Katz p-adic L-functions and congruence modules, Ann. Sci. École Norm. Sup.26 (1993) 189-259. Zbl0778.11061MR1209708
- [27] Illusie L., Réduction semi-stable et décomposition de complexes de de Rham à coefficients, Duke Math. J.60 (1990) 139-185. Zbl0708.14014MR1047120
- [28] Jantzen J., Representations of Algebraic Groups, Academic Press, New York, 1987. Zbl0654.20039MR899071
- [29] M. Kisin, K. Lai, Overconvergent Hilbert modular forms, Amer. J. Math., submitted for publication. Zbl1129.11020MR2154369
- [30] Mazur B., Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math.47 (1977) 33-186. Zbl0394.14008MR488287
- [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. Zbl1078.11037MR1944174
- [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. Zbl0748.14008MR1149032
- [33] Polo P., Tilouine J., Bernstein–Gelfand–Gelfand complexes and cohomology of nilpotent groups over for representations withp-small weights, in: Cohomology of Siegel Varieties, Astérisque, vol. 280, 2002, pp. 97-135. Zbl1035.17030MR1944175
- [34] Rapoport M., Compactification de l'espace de modules de Hilbert–Blumenthal, Compositio Math.36 (1978) 255-335. Zbl0386.14006MR515050
- [35] Ribet K., On l-adic representations attached to modular forms, Invent. Math.28 (1975) 245-275. Zbl0302.10027MR419358
- [36] Ribet K., Mod p Hecke operators and congruences between modular forms, Invent. Math.71 (1983) 193-205. Zbl0508.10018MR688264
- [37] Serre J.-P., Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math.15 (1972) 259-331. Zbl0235.14012MR387283
- [38] Shimura G., The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J.45 (1978) 637-679. Zbl0394.10015MR507462
- [39] Steinberg R., Representations of algebraic groups, Nagoya Math. J.22 (1963) 33-56. Zbl0271.20019MR155937
- [40] Taylor R., On Galois representations associated to Hilbert modular forms, Invent. Math.98 (1989) 265-280. Zbl0705.11031MR1016264
- [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. Zbl0836.11017MR1363502
- [42] Wedhorn T., Congruence relations on some Shimura varieties, J. reine angew. Math.524 (2000) 43-71. Zbl1101.14033MR1770603
- [43] Wiles A., On ordinary λ-adic representations associated to modular forms, Invent. Math.94 (1988) 529-573. Zbl0664.10013
- [44] Yoshida H., On the zeta functions of Shimura varieties and periods of Hilbert modular forms, Duke Math. J.74 (1994) 121-191. Zbl0823.11018MR1284818
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