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Book Review
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Book Information
Author(s):
Haruzo Hida
Title:
-Adic automorphic forms on Shimura varieties
Additional book information:
Springer-Verlag,
New York,
2004,
xii+390,
US$99.00,
0-387-20711-2
References:
-
- [B]
- A. I. Badulescu, Unitary representations and global Jacquet-Langlands correspondence, preprint.
- [BM]
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- [BW]
- A. Borel and N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Ann. Math. Studies, Princeton University Press, 1980. MR 0554917 (83c:22018)
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- J-M. Fontaine, Modular forms and Fermat's Last Theorem (G. Cornell, J. H. Silverman, G. Stevens, eds.), Springer-Verlag, 1991; H. Darmon, F. Diamond and R. Taylor, Fermat's Last Theorem, Current developments in mathematics, 1995 (R. Bott, A. Jaffe, S. T. Yau, eds.), International Press, 1994. MR 1474977 (99d:11067a)
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-adiques, Sém. de Bures, 1988, Astérisque 223, 1994. MR 1274489 (94m:14004) - [FP]
- J-M. Fontaine and B. Perrin-Riou, Cohomologie galoisienne et valeurs de fonctions
, [Mo]. - [Gr]
- R. Greenberg, Iwasawa theory for
-adic representations, Algebraic number theory - in honor of K. Iwasawa, Adv. Studies in Pure Math., 17 (H. Morikawa, ed.), Academic Press, 1989; Iwasawa theory and -adic deformations of motives, [Mo]. MR 1097613 (92c:11116) - [GS]
- P. Griffiths and W. Schmid, Recent developments in Hodge theory: A discussion of techniques and results, Proc. of International Colloquium on discrete subgroups of Lie groups & applications to moduli, Oxford Univ. Press, 1975. MR 0419850 (54:7868)
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- G. Harder, Eisensteinkohomologie und die Konstruktion gemischter Motive, SLN 1562, Springer-Verlag, 1993. MR 1285354 (95g:11043)
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- H. Hida, Congruences of cusp forms and Hecke algebras, Séminaire de Théorie des Nombres, Paris 1983-84, Prog. in Math., vol. 59, Birkhäuser, 1985; Galois representations into
attached to ordinary cusp forms, Inv. Math. 85 (1986), 545-613. MR 0902830 (89a:11052), MR 0848685 (87k:11049) - [Kh]
- Chandrasekhar Khare, Serre's modularity conjecture, preprint.
- [Ki]
- M. Kisin, Moduli of finite flat group schemes and modularity, preprint, Univ. of Chicago.
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- N. Katz, J-P. Serre and H.P.F. Swinnerton-Dyer, Modular functions of one variable III, SLM 350, Springer-Verlag, 1973. MR 0323724 (48:2080)
- [L]
- R. P. Langlands, Beyond Endoscopy, Contributions to automorphic forms, geometry & number theory (H. Hida, D. Ramakrishnan and F. Shahidi, eds.), The Johns Hopkins Univ. Press, 2004; Un nouveau point de repère dans la théorie des formes automorphes, preprint. MR 2058599 (2005a:11002)
- [LM]
- R. P. Langlands, The representation theory of abelian algebraic groups, Pacific Jour. of Math. 61 (1998); J. S. Milne, Arithmetic duality theorems, Perspectives in Mathematics, No. 1, Academic Press, 1986. MR 0881804 (88e:14028)
- [LS]
- R. Langlands, Automorphic representations, Shimura varieties, and motives, Automorphic forms, representations and
-functions, Proc. Symp. Pure Math., vol. XXXIII, Amer. Math. Soc., 1979; J. Milne and K.Y. Shih, Langlands' construction of the Taniyama group, Hodge cycles, motives and Shimura varieties, Springer-Verlag, 1982; J-P. Serre, Propriétés conjecturales des groupes de Galois motiviques et des représentations -adiques, [Mo]. MR 0546619 (83f:12010), MR 0654325 (84m:14046) - [Mo]
- B. Mazur, Motives, Parts 1,2 (U. Jannsen, S. Kleiman, J-P. Serre, eds.), Amer. Math. Soc., 1994. MR 1265518 (94i:11003)
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- B. Mazur and A. Wiles, Class fields of abelian extensions of
, Invent. Math. 76 (1984), 179-330; J. Coates, The work of Mazur and Wiles on cyclotomic fields, Sém. Bourbaki, vol. 1980/81, SLN 901, Springer-Verlag, 1981. MR 0742853 (85m:11069), MR 0647499 (83i:12005) - [R]
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-adic lifts of automorphic mod representations, preprint; R. Taylor, Automorphy for some -adic lifts of automorphic mod representations, II, preprint. MR 2060030 (2005a:11071) - [Ti]
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Additional Information:
Reviewer(s):
R.
P.
Langlands
Affiliation:
Institute for Advanced Study
Email:
rpl@math.ias.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
44
(2007),
291-308.
MSC
(2000):
Primary 11G18, 14G10
DOI:
10.1090/S0273-0979-06-01131-1
PII:
S 0273-0979(06)01131-1
Posted:
October 18, 2006
Copyright of article:
Copyright
2006,
R. P. Langlands
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