p-adic automorphic forms on reductive groups
Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000, Astérisque, no. 298 (2005), pp. 147-254.
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     author = {Hida, Haruzo},
     title = {$p$-adic automorphic forms on reductive groups},
     booktitle = {Formes automorphes (I) - Actes du semestre du centre \'Emile Borel, printemps 2000},
     editor = {Tilouine Jacques and Carayol Henri and Harris Michael and Vign\'eras Marie-France},
     series = {Ast\'erisque},
     pages = {147--254},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {298},
     year = {2005},
     mrnumber = {2141703},
     zbl = {1122.11026},
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Hida, Haruzo. $p$-adic automorphic forms on reductive groups, in Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000, Astérisque, no. 298 (2005), pp. 147-254. http://www.numdam.org/item/AST_2005__298__147_0/

[AAF] G. Shimura - Arithmeticity in the Theory of Automorphic Forms, Mathematical Surveys and Monographs, vol. 82, American Mathematical Society, 2000. | MR | Zbl

[ABV] D. Mumford - Abelian Varieties, TIFR Studies in Mathematics, Oxford University Press, 1994. | MR | Zbl

[ACM] G. Shimura - Abelian Varieties with Complex Multiplication and Modular Functions, Princeton University Press, 1998. | DOI | MR | Zbl

[ALG] R. Hartshorne - Algebraic Geometry, Graduate Texts in Math., vol. 52, Springer, 1977. | DOI | MR | Zbl

[AME] N. M. Katz & B. Mazur - Arithmetic Moduli of Elliptic Curves, Annals of Math. Studies, vol. 108, Princeton University Press, 1985. | MR | Zbl

[BCM] N. Bourbaki - Algèbre Commutative, Hermann, Paris, 1961-65. | Zbl

[CBT] W. Messing - The Crystals Associated to Barsotti-Tate Groups; With Applications to Abelian Schemes, Lect. Notes in Math., vol. 264, Springer, New York, 1972. | MR | Zbl

[CRT] H. Matsumura - Commutative Ring Theory, Cambridge studies in advanced mathematics, vol. 8, Cambridge University Press, Cambridge, 1986. | MR | Zbl

[CSM] C.-L. Chai - Compactification of Siegel Moduli Schemes, LMS Lecture note series, vol. 107, Cambridge University Press, Cambridge, 1985. | MR | Zbl

[DAV] G. Faltings & C.-L. Chai - Degeneration of Abelian Varieties, Springer, 1990. | DOI | MR | Zbl

[EGA] A. Grothendieck & J. Dieudonné - Eléments de Geometrie Algébrique, Publ. Math. Inst. Hautes Etudes Sci., vol. 4, 1960. | DOI | Numdam | Zbl

A. Grothendieck & J. Dieudonné - Eléments de Geometrie Algébrique, Publ. Math. Inst. Hautes Etudes Sci., vol. 8, 1961. | Numdam

A. Grothendieck & J. Dieudonné - Eléments de Geometrie Algébrique, Publ. Math. Inst. Hautes Etudes Sci., vol. 11, 1961. | Numdam

A. Grothendieck & J. Dieudonné - Eléments de Geometrie Algébrique, Publ. Math. Inst. Hautes Etudes Sci., vol. 17, 1963. | Numdam

A. Grothendieck & J. Dieudonné - Eléments de Geometrie Algébrique, Publ. Math. Inst. Hautes Etudes Sci., vol. 20, 1964. | Numdam

A. Grothendieck & J. Dieudonné - Eléments de Geometrie Algébrique, Publ. Math. Inst. Hautes Etudes Sci., vol. 24, 1965. | Numdam

A. Grothendieck & J. Dieudonné - Eléments de Geometrie Algébrique, Publ. Math. Inst. Hautes Etudes Sci., vol. 28, 1966. | DOI | Numdam

A. Grothendieck & J. Dieudonné - Eléments de Geometrie Algébrique, Publ. Math. Inst. Hautes Etudes Sci., vol. 32, 1967. | Numdam

[EPE] G. Shimura - Euler Products and Eisenstein Series, CBMS Regional Conference Series, vol. 93, American Mathematical Society, Providence, RI, 1997. | DOI | MR | Zbl

[GIT] D. Mumford - Geometric Invariant Theory, Ergebnisse, vol. 34, Springer, 1965. | MR | Zbl

[GME] H. Hida - Geometric Modular Forms and Elliptic Curves, World Scientific Publishing Co., Singapore, 2000. | DOI | MR | Zbl

[IAT] G. Shimura - Introduction to the Arithmetic Theory of Automorphic Functions, Princeton University Press and Iwanami Shoten, Princeton & Tokyo, 1971. | MR | Zbl

[LFE] H. Hida - Elementary Theory of L-functions and Eisenstein Series, LMSST, vol. 26, Cambridge University Press, Cambridge, 1993. | MR | Zbl

[MFG] H. Hida, Modular Forms and Galois Cohomology, Cambridge studies in advanced mathematics, vol. 69, Cambridge University Press, Cambridge, 2000. | MR | Zbl

[PAF] H. Hida, p-Adic Automorphic Forms on Shimura Varieties, Springer Monographs in Mathematics, Springer, New York, 2004. | DOI | MR | Zbl

[RAG] J. C. Jantzen - Representations of Algebraic Groups, Academic Press, 1987. | MR | Zbl

[BZ] I. N. Bernstein & A. V. Zelevinsky - Induced representations of reductive 𝔭-adic groups, I, Ann. scient. Éc. Norm. Sup. 4e série 10 (1977), p. 441-472. | DOI | EuDML | Numdam | MR | Zbl

[C] C.-L. Chai - Arithmetic minimal compactification of the Hilbert-Blumenthal moduli spaces, Ann. of Math. 131 (1990), p. 541-554. | DOI | MR | Zbl

[D] P. Deligne - Variété abeliennes ordinaires sur un corps fini, Invent. Math. 8 (1969), p. 238-243. | DOI | EuDML | MR | Zbl

[D1] P. Deligne, Travaux de Shimura, in Séminaire Bourbaki, Lect. Notes in Math., vol. 244, Springer, 1971, Exp. n° 389, p. 123-165. | EuDML | Numdam | MR | Zbl

[D2] P. Deligne, Variétés de Shimura: interprétation modulaire, et techniques de construction de modèles canoniques, Proc. Symp. Pure Math., vol. 33.2, American Mathematical Society, 1979, p. 247-290. | DOI | MR | Zbl

[DM] P. Deligne & D. Mumford - The irreducibility of the space of curves of given genus, Publ. Math. Inst. Hautes Études Sci. 36 (1969), p. 75-109. | DOI | EuDML | Numdam | MR | Zbl

[DR] P. Deligne & K. A. Ribet - Values of abelian L-functions at negative integers over totally real fields, Invent. Math. 59 (1980), p. 227-286. | DOI | EuDML | MR | Zbl

[DT] M. Dimitrov & J. Tilouine - Variétés et formes modulaires de Hilbert arithmétiques pour Γ 1 (𝔠,𝔫), in Geometric aspects of Dwork theory, Vol. II (A. Adolphson, F. Baldassarri, P. Berthelot, N. Katz & F. Loeser, eds.), Walter de Gruyter GmbH & Co. KG, Berlin, 2004, p. 555-614. | MR | Zbl

[Du] M. Deuring - Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abhandlungen Math. Sem. Hansischen Universität 14 (1941), p. 197-272. | DOI | JFM | MR | Zbl

[F] K. Fujiwara - Arithmetic compactifications of Shimura varieties, Master thesis, University of Tokyo, 1989.

[G] B. B. Gordon - Canonical models of Picard modular surfaces, CRM Publications, vol. 13, 1992, p. 1-29. | MR | Zbl

[H86a] H. Hida - Iwasawa modules attached to congruences of cusp forms, Ann. scient. Éc. Norm. Sup. 4e série 19 (1986), p. 231-273. | DOI | EuDML | Numdam | MR | Zbl

[H86b] H. Hida, Galois representations into GL 2 ( p X) attached to ordinary cusp forms, Invent. Math. 85 (1986), p. 545-613. | DOI | EuDML | MR | Zbl

[H88] H. Hida, On p-adic Hecke algebras for GL 2 over totally real fields, Ann. of Math. 128 (1988), p. 295-384. | DOI | MR | Zbl

[H95] H. Hida, Control theorems of p-ordinary cohomology groups for SL(n), Bull. Soc. math. France 123 (1995), p. 425-475. | DOI | EuDML | Numdam | MR | Zbl

[H96] H. Hida, On the search of genuine p-adic modular L-functions for GL(n), Mém. Soc. math. France (N.S.), vol. 67, Société Mathématique de France, 1996, preprint downloadable at www.math.ucla.edu/~hida. | EuDML | Numdam | MR | Zbl

[H02] H. Hida, Control theorems of coherent sheaves on Shimura varieties of PEL-type, J. Inst, of Math. Jussieu 1 (2002), p. 1-76, preprint downloadable at www.math.ucla.edu/~hida. | DOI | MR | Zbl

[HM] H. Hida & Y. Maeda - Non-abelian base change for totally real fields, Pacific J. Math. (1998), p. 189-217, special issue, preprint downloadable at www.math.ucla. edu/~hida. | MR | Zbl

[HT] H. Hida & J. Tilouine - Anticyclotomic Katz p-adic L-functions and congruence modules, Ann. scient. Éc. Norm. Sup. 4e série 26 (1993), p. 189-259. | DOI | EuDML | Numdam | MR | Zbl

[I] J. Igusa - Kroneckerian model of fields of elliptic modular functions, Amer. J. Math. 81 (1959), p. 561-577. | DOI | MR | Zbl

[K] N. M. Katz - Serre-Tate local moduli, in Surfaces Algébriques, Lect. Notes in Math., vol. 868, Springer, 1978, p. 138-202. | DOI | MR | Zbl

[K1] N. M. Katz, Higher congruences between modular forms, Ann. of Math. 101 (1975), p. 332-367. | DOI | MR | Zbl

[K2] N. M. Katz, p-adic L-functions for CM fields, Invent. Math. 49 (1978), p. 199-297. | DOI | EuDML | MR | Zbl

[K3] N. M. Katz, p-adic properties of modular schemes and modular forms, Lect. Notes in Math., vol. 350, Springer, 1973, p. 70-189. | MR | Zbl

[Ko] R. Kottwitz - Points on Shimura varieties over finite fields, J. Amer. Math. Soc. 5 (1992), p. 373-444. | DOI | MR | Zbl

[L] M. J. Larsen - Arithmetic compactification of some Shimura surfaces, CRM Publications, vol. 13, 1992, p. 31-45. | MR | Zbl

[MiS] J. Milne & K. Y. Shih - Automorphism groups of Shimura varieties and reciprocity laws, Amer. J. Math. 103 (1981), p. 911-935. | DOI | MR | Zbl

[Mik] K. Miyake - Models of certain automorphic function fields, Acta Math. 126 (1971), p. 245-307. | DOI | MR | Zbl

[Mit] T. Miyake - On automorphism groups of the fields of automorphic functions, Ann. of Math. 95 (1972), p. 243-252. | DOI | MR | Zbl

[Mo] D. Mauger - Algébres de Hecke quasi-ordinaires universelles, Ann. scient. Éc. Norm. Sup. 4e série 37 (2004), p. 171-222. | DOI | EuDML | Numdam | MR | Zbl

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

[Ri] K. A. Ribet - P-adic interpolation via Hilbert modular forms, Proc. Symp. Pure Math., vol. 29, American Mathematical Society, 1975, p. 581-592. | DOI | MR | Zbl

[Sc] A. J. Scholl - Motives for modular forms, Invent. Math. 100 (1990), p. 419-430. | DOI | EuDML | MR | Zbl

[Sh1] G. Shimura - On analytic families of polarized abelian varieties and automorphic functions, Ann. of Math. 78 (1963), p. 149-192. | DOI | MR | Zbl

[Sh2] G. Shimura, Moduli and fibre system of abelian varieties, Ann. of Math. 83 (1966), p. 294-338. | DOI | MR | Zbl

[Sh3] G. Shimura, On canonical models of arithmetic quotients of bounded symmetric domains, Ann. of Math. 91 (1970), p. 144-222. | DOI | MR | Zbl

G. Shimura, On canonical models of arithmetic quotients of bounded symmetric domains, Ann. of Math. II, 92 (1970), p. 528-549. | DOI | MR | Zbl

[Sh4] G. Shimura, On some arithmetic properties of modular forms of one and several variables, Ann. of Math. 102 (1975), p. 491-515. | DOI | MR | Zbl

[TiU] J. Tilouine & E. Urban - Several-variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations, Ann, scient. Éc. Norm. Sup. 4e série 32 (1999), p. 499-574. | DOI | EuDML | Numdam | MR | Zbl

[Tt] J. Tits - Reductive groups over local fields, in Automorphic forms, representations and L-functions, Proc. Symp. Pure Math., vol. 33.1, American Mathematical Society. 1979, p. 29-69. | DOI | MR | Zbl