Several-variable $p$-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations

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1. [1] A. ASH and G. STEVENS, p-adic deformations of cohomology classes of subgroups of GL(n, Z), Coll. Math. 48, Proc. Journées Arithmétiques, 1995, Barcelone. Zbl0866.20038MR98h:11064
2. [2] A. BOREL and J-P. SERRE, Corners and arithmetic groups, Comment. Math. Helv., 48, 1973, pp. 436-491. Zbl0274.22011MR52 #8337
3. [3] A. BOREL and N. WALLACH, Continuous cohomology, discrete subgroups and representations of reductive groups, Ann. of Math. Stud., 94, Princeton Univ. Press, Princeton, 1980. Zbl0443.22010MR83c:22018
4. [4] N. BOURBAKI, Commutative algebra, Chapters 1-7, Addison Wesley, 1972. MR50 #12997
5. [5] K. BUECKER, Congruences between Siegel modular forms on the level of group cohomology, Ann. Inst. Fourier (Grenoble), 46, 1996. Zbl0853.11038MR98f:11038
6. [6] K. BUECKER, On the control theorem for the symplectic group, Compositio Math., 113, 1998. Zbl0923.11076MR99m:11056
7. [7] C.-L. CHAI and G. FALTINGS, Degeneration of abelian varieties, Erg. Math. 3. Folge Band 22, Springer-Verlag, 1990. Zbl0744.14031MR92d:14036
8. [8] J. FRANKE, Harmonic Analysis in weighted L²-spaces, Ann. Éc. Norm. Sup., 4ième Série, t. 31, 1998, p. 181-279. Zbl0938.11026MR2000f:11065
9. [9] G. FALTINGS, Crystalline cohomology and Galois representations in Algebraic Analysis, Geometry and Number Theory, Proceedings of JAMI Inaugural Conference, John Hopkins Univ. Press, 1989. Zbl0805.14008MR98k:14025
10. [10] J.M FONTAINE, Représentations p-adiques semi-stables, Séminaire de Bures sur les périodes p-adiques, Astérisque, 223, SMF, Paris, 1994. Zbl0865.14009
11. [11] R. GODEMENT, Topologie algébrique et théorie des faisceaux, Hermann Paris (1964). 
12. [12] H. HIDA, On congruence divisors of cusp forms as factors of the special values of their zeta functions, Inv. Math., 64, 1981, pp. 221-262. Zbl0472.10028MR83h:10066
13. [13] H. HIDA, Galois representations into GL2(Zp[[X]]) attached to ordinary cusp forms, Inv. math., 85, 1986, pp. 545-613. Zbl0612.10021MR87k:11049
14. [14] H. HIDA, Modules of Congruences of Hecke algebras and L-functions associated with cusp forms, Amer. J. of Math., 110, 1988, pp. 323-382. Zbl0645.10029MR89i:11058
15. [15] H. HIDA, Nearly ordinary Hecke algebras and several variables Galois representations, pp. 115-134, in Algebraic Analysis, Geometry and Number Theory, Proc. of the JAMI inaugural conference, ed. J.-I. Igusa, Johns Hopkins Univ. Press, Baltimore, 1990. Zbl0782.11017
16. [16] H. HIDA, p-Ordinary cohomology groups for SL(2) for number fields. Duke Math. J., Vol. 69, No. 2, 1993. Zbl0941.11024MR94g:11031
17. [17] H. HIDA, Control Theorems of p-nearly ordinary Cohomology Groups for SL(n), Bull. Soc. Math. France, 123, 1995, pp. 425-475. Zbl0852.11023MR97c:11053
18. [18] H. HIDA, Automorphic induction for GLn and the Leopoldt conjecture, preprint 1994. 
19. [19] H. HIDA, Control theorems of coherent sheaves on Shimura varieties of PEL-type, preprint. Zbl1039.11041
20. [20] H. HIDA, J. TILOUINE and E. URBAN, Adjoint Modular Galois representations and their Selmer groups, Proc. Conf. Nat. Acad. Sci. USA, vol. 94, pp. 111121-11124, Oct. 1997. Zbl0909.11025MR98m:11034
21. [21] N. IWAHORI and H. MATSUMOTO, On some Bruhat decompositions and the structure of the Hecke rings of p-adic Chevalley groups, Publ. Math. IHES, 1965, pp. 237-280. Zbl0228.20015MR32 #2486
22. [22] J.C. JANTZEN, Representations of Algebraic Groups, Academic Press, 1987. Zbl0654.20039MR89c:20001
23. [23] G. LAUMON, Sur la cohomologie à supports compacts des variétés de Shimura pour GSp(4)Q, Comp. Math., vol. 105, 1996, pp. 267-359. Zbl0877.11037MR2000a:11097
24. [24] A. MOKRANE and J. TILOUINE, Modulo p crystalline BGG and freeness of the cohomology modules, preprint. Zbl1078.11037
25. [25] L. NYSSEN, Pseudo-représentations, Math. Ann., 306, 1996, pp. 257-283. Zbl0863.16012MR98a:20013
26. [26] B. PERRIN-RIOU, Représentations galoisiennes ordinaires, Séminaire de Bures sur les périodes p-adiques, Astérisque, 223, SMF, Paris 1994. Zbl0838.11071
27. [27] J. SCHWERMER, On arithmetic quotients of the Siegel upper helf space of degree two, Comp. Math., 58, 1986, pp. 233-258. Zbl0596.10029MR87j:11040
28. [28] J. SCHWERMER, letter to the authors, Sept. 28, 1995. 
29. [29] J. SCHWERMER, Kohomologie arithmetisch definierter Gruppen und Eisensteinreihen, Lect. Notes 988. Berlin-Heidelberg-New York-Tokyo, Springer, 1983. Zbl0506.22015MR87i:22034
30. [30] S. SEN, Continuous cohomology and p-Adic Galois Representations, Inv. Math., 62, 1980, pp. 89-116. Zbl0463.12005MR82e:12018
31. [31] S. SEN, An Infinite dimensional Hodge-Tate theory, Bull. Soc. Math. France, 121, 1993, pp. 13-34. Zbl0786.11067MR94e:11121
32. [32] G. SHIMURA, On modular correspondences for Sp(N, Z) and their congruence relations, Proc. Nat. Acad. Sci., 49, 1963, pp. 824-828. Zbl0122.08803MR28 #250
33. [33] R. TAYLOR, Galois representations associated to Siegel modular forms of low weight, Duke Math. J., 63, 1991, pp. 281-332. Zbl0810.11033MR92j:11044
34. [34] R. TAYLOR, On the l-adic cohomology of Siegel threefolds, Inv. Math., 114, 1993, pp. 289-310. Zbl0810.11034MR95j:11054
35. [35] R. TAYLOR and A. WILES, Ring-theoretical properties of certain Hecke algebras, Annals of Math., 141, 1995, pp. 553-572. Zbl0823.11030MR96d:11072
36. [36] J. TILOUINE, Deformations of Galois representations and Hecke algebras, Publ. Mehta Res. Inst., Narosa Publ., New Delhi, 1996. Zbl1009.11033MR99i:11038
37. [37] J. TILOUINE, Deformations of Siegel-Hilbert Hecke eigensystems and their Galois representations, in Proc. of the Tiruchirapalli Conference, eds. K. Murty and M. Waldschmidt, Publ. AMS, Cont. Math. 210, 1998. Zbl1020.11036MR99a:11067
38. [38] J. TILOUINE and E. URBAN, Familles p-adiques à trois variables de formes de Siegel et de représentations galoisiennes, C.R.A.S. Paris, t. 321, Série I, 1995, pp. 5-10. Zbl1019.11502MR96c:11048
39. [39] E. URBAN, Module de congruences pour GL2 d'un corps quadratique imaginaire et théorie d'Iwasawa d'un corps CM biquadratique, Duke Math. J., vol. 92, No 1, 1998, pp. 179-220. Zbl0973.11095MR98m:11035
40. [40] E. URBAN, Selmer group and the Eisenstein-Klingen Ideal, preprint, 1997. 
41. [41] E. URBAN, Letter to J. Tilouine, Nov. 1997. 
42. [42] E. URBAN, Sur les représentations p-adiques associées aux représentations cuspidales de GSp4Q, in preparation. 
43. [43] D. VOGAN, Representations of Real Reductive Lie Groups, Progress in Mathematics 15, Birkhäuser, 1981. Zbl0469.22012MR83c:22022
44. [44] D. VOGAN and G. ZUCKERMAN, Unitary representations with non-zero cohomology, Comp. Math., 53, 1984, pp. 51-90. Zbl0692.22008MR86k:22040
45. [45] J.-L. WALDSPURGER, Cohomologie des espaces de formes automorphes d'après Franke, Séminaire Bourbaki Novembre 1995, exp.809. Zbl0883.11025
46. [46] R. WEISSAUER, A special case of the fundamental lemma : the case GSp4, I, II, III, preprints. 
47. [47] A. WILES, On p-adic representations for totally real fields, Ann. of Math., 123, 1986, pp. 407-456. Zbl0613.12013MR87g:11142
48. [48] A. WILES, Modular curves and Fermat's Last Theorem, Ann. of Math., 123, 1995. Zbl0823.11029

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