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Book Information:
Author:
Haruzo Hida
Title:
-Adic automorphic forms on Shimura varieties
Additional book information:
Springer-Verlag,
New York,
2004,
xii+390 pp.,
ISBN 0-387-20711-2,
US$99.00$
[B] A. I. Badulescu, Unitary representations and global Jacquet-Langlands correspondence, preprint.
M. V. Borovoĭ, Conjugation of Shimura varieties, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 783–790. MR 934281
Armand Borel and Nolan R. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Annals of Mathematics Studies, No. 94, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 554917
Henri Darmon, Fred Diamond, and Richard Taylor, Fermat’s last theorem, Current developments in mathematics, 1995 (Cambridge, MA), Int. Press, Cambridge, MA, 1994, pp. 1–154. MR 1474977
S. Ramanan and Arnaud Beauville (eds.), Proceedings of the Indo-French Conference on Geometry, Hindustan Book Agency, Delhi, 1993. Held in Bombay, 1989. MR 1274489
[FP] J-M. Fontaine and B. Perrin-Riou, Cohomologie galoisienne et valeurs de fonctions 
, [Mo].
Ralph Greenberg, Iwasawa theory for $p$-adic representations, Algebraic number theory, Adv. Stud. Pure Math., vol. 17, Academic Press, Boston, MA, 1989, pp. 97–137. MR 1097613, DOI 10.2969/aspm/01710097
Phillip Griffiths and Wilfried Schmid, Recent developments in Hodge theory: a discussion of techniques and results, Discrete subgroups of Lie groups and applicatons to moduli (Internat. Colloq., Bombay, 1973) Oxford Univ. Press, Bombay, 1975, pp. 31–127. MR 0419850
Günter Harder, Eisensteinkohomologie und die Konstruktion gemischter Motive, Lecture Notes in Mathematics, vol. 1562, Springer-Verlag, Berlin, 1993 (German). MR 1285354, DOI 10.1007/BFb0090305
Haruzo Hida, Congruences of cusp forms and Hecke algebras, Séminaire de théorie des nombres, Paris 1983–84, Progr. Math., vol. 59, Birkhäuser Boston, Boston, MA, 1985, pp. 133–146. MR 902830, DOI 10.1007/BF01581241
[Kh] Chandrasekhar Khare, Serre's modularity conjecture, preprint.
[Ki] M. Kisin, Moduli of finite flat group schemes and modularity, preprint, Univ. of Chicago.
Willem Kuyk and J.-P. Serre (eds.), Modular functions of one variable. III, Lecture Notes in Mathematics, Vol. 350, Springer-Verlag, Berlin-New York, 1973. MR 0323724
Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi (eds.), Contributions to automorphic forms, geometry, and number theory, Johns Hopkins University Press, Baltimore, MD, 2004. Papers from the conference in honor of Joseph Shalika held at Johns Hopkins University, Baltimore, MD, May 14–17, 2002. MR 2058599
J. S. Milne, Arithmetic duality theorems, Perspectives in Mathematics, vol. 1, Academic Press, Inc., Boston, MA, 1986. MR 881804
R. P. Langlands, Automorphic representations, Shimura varieties, and motives. Ein Märchen, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 205–246. MR 546619
Uwe Jannsen, Steven Kleiman, and Jean-Pierre Serre (eds.), Motives, Proceedings of Symposia in Pure Mathematics, vol. 55, American Mathematical Society, Providence, RI, 1994. MR 1265518, DOI 10.1090/pspum/055.1
B. Mazur and A. Wiles, Class fields of abelian extensions of $\textbf {Q}$, Invent. Math. 76 (1984), no. 2, 179–330. MR 742853, DOI 10.1007/BF01388599
Karl Rubin, The “main conjectures” of Iwasawa theory for imaginary quadratic fields, Invent. Math. 103 (1991), no. 1, 25–68. MR 1079839, DOI 10.1007/BF01239508
J. T. Tate, $p$-divisible groups, Proc. Conf. Local Fields (Driebergen, 1966) Springer, Berlin, 1967, pp. 158–183. MR 0231827
Richard Taylor, Galois representations, Ann. Fac. Sci. Toulouse Math. (6) 13 (2004), no. 1, 73–119 (English, with English and French summaries). MR 2060030
[Ti] J. Tilouine, Galois representations congruent to those coming from Shimura varieties, [Mo].
André Weil, On a certain type of characters of the idèle-class group of an algebraic number-field, Proceedings of the international symposium on algebraic number theory, Tokyo & Nikko, 1955, Science Council of Japan, Tokyo, 1956, pp. 1–7. MR 0083523
- [B]
- A. I. Badulescu, Unitary representations and global Jacquet-Langlands correspondence, preprint.
- [BM]
- M. V. Borovoi, Conjugation of Shimura varieties, Proc. of Int. Cong. Math., Berkeley, 1986, Amer. Mat. Soc., 1987; J.S. Milne, Introduction to Shimura varieties, Harmonic analysis, the trace formula and Shimura varieties (J. Arthur, R. Kottwitz, eds.), Amer. Math. Soc., 2005. MR 0934281 (89h:11025), MR 2192012
- [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)
- [F]
- 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)
- [FI]
- J-M. Fontaine et al., Proceedings of the Indo-French conference on geometry, Hindustan Book Agency, 1993; , Périodes
-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)
- [Ha]
- G. Harder, Eisensteinkohomologie und die Konstruktion gemischter Motive, SLN 1562, Springer-Verlag, 1993. MR 1285354 (95g:11043)
- [Hi]
- 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
![$ GL_{2}(\mathbb{Z}_{p}[[X]])$](/bull/2007-44-02/S0273-0979-06-01131-1/gif-references0/img5.gif)
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.
- [KS]
- 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)
- [MW]
- 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]
- K. Rubin, The ``main conjectures'' of Iwasawa theory for imaginary quadratic fields, Invent. Math. 103 (1991), 25-68. MR 1079839 (92f:11151)
- [T]
- J.T. Tate,
-divisible groups, Local fields, Springer-Verlag, 1967. MR 0231827 (38:155)
- [Ta]
- R. Taylor, Galois representations, Ann. Fac. Sci. Toulouse (6) 13 (2004), 73-119; L. Clozel, M. Harris and R. Taylor, Automorphy for some
-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]
- J. Tilouine, Galois representations congruent to those coming from Shimura varieties, [Mo].
- [W]
- A. Weil, On a certain type of character of the idèle-class group of an algebraic number-field, Proc. Int. Symp. on Alg. Number Theory, Tokyo & Nikko, 1955, pp. 1-7. MR 0083523 (18:720e)
Review Information:
Reviewer:
R. P. Langlands
Affiliation:
Institute for Advanced Study
Email:
rpl@math.ias.edu
Journal:
Bull. Amer. Math. Soc.
44 (2007), 291-308
Published electronically:
October 18, 2006
Review copyright:
© Copyright 2006
R. P. Langlands
