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Book Review

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Book Information

Author(s): Michael Harris and Richard Taylor
Title: The geometry and cohomology of some simple Shimura varieties
Additional book information: with an appendix by Vladimir G. Berkovich, Annals of Mathematics Studies, Number 151, Princeton University Press, Princeton, NJ, 2001, viii + 276, $35.00 (paperback), ISBN 0-691-09092-0; $65.00 (cloth), ISBN 0-691-09090-4

References:

1.
H. Carayol, Preuve de la conjecture de Langlands locale pour $GL_n$: travaux de Harris-Taylor et Henniart. Sém. Bourbaki no. 857. Astérisque no. 266, SMF, Paris (2000), 191-244. MR 2001i:11136

2.
P. Deligne, Les constantes des équations functionelles des functions $L$. Modular Forms II, Lecture Notes in Math. 349, Springer-Verlag (1973), 501-595. MR 50:2128
3.
M. Harris, On the local Langlands correspondence. To appear in Proc. of the Beijing ICM, 2002. Also available at http://www.math.jussieu.fr/~harris.

4.
G. Henniart, Caractérisation de la correspondence de Langlands par les facteurs $\varepsilon$ de paires. Invent. Math. 113 (1993), 339-350. MR 96e:11078

5.
G. Henniart, Une preuve simple des conjectures de Langlands pour $GL(n)$ sur un corps $p$-adique. Invent. Math. 139 (2000), 439-455. MR 2001e:11052

6.
G. Henniart, A report on the proof of the Langlands conjectures for $GL(N)$ over $p$-adic fields. Current Developments in Mathematics 1999. International Press (1999).
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G. Henniart, Sur la conjecture de Langlands locale pour $GL_n$. J. Théor. Nombres Bordeaux 13 (2001), no. 1, 167-187. MR 2002f:11178
8.
H. Jacquet, I. I. Piatetski-Shapiro, J. Shalika, Rankin-Selberg convolutions. Amer. J. Math. 105 (1983), 367-483. MR 85g:11044

9.
R. Taylor, Galois Representations. Preprint. Available at http://www.math.harvard. edu/rtaylor.
10.
A. V. Zelevinsky, Induced representations of reductive $p$-adic groups: on irreducible representations of $GL(n)$. Ann. Scient. Éc. Norm. Sup. (4) 13 (1980), 165-210. MR 83g:22012

Additional Information:

Reviewer(s):
Alan Roche
Affiliation: University of Oklahoma
Email: aroche@math.ou.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 40 (2003), 239-246.

MSC (2000): Primary 11G18, 11F70, 14G35, 22E50
DOI: 10.1090/S0273-0979-03-00977-7
PII: S 0273-0979(03)00977-7
Posted: February 12, 2003
Copyright of article: Copyright 2003, American Mathematical Society

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