Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Retrieve article in: PDF DVI PostScript

Book Information

Author(s): Haruzo Hida
Title: $ p$-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]
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 $ p$-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 $ L$, [Mo].

[Gr]
R. Greenberg, Iwasawa theory for $ p$-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 $ p$-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]])$ 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 $ L$-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 $ l$-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 $ \mathbb{Q}$, 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, $ p$-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 $ l$-adic lifts of automorphic mod $ l$ representations, preprint; R. Taylor, Automorphy for some $ l$-adic lifts of automorphic mod $ l$ 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)


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


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google