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Book Review

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Book Information:

Authors: 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 pp., ISBN 0-691-09092-0, $35.00, paperback; ISBN 0-691-09090-4, $65.00, cloth

References [Enhancements On Off] (What's this?)

  • 1. Henri Carayol, Preuve de la conjecture de Langlands locale pour 𝐺𝐿_{𝑛}: travaux de Harris-Taylor et Henniart, Astérisque 266 (2000), Exp. No. 857, 4, 191–243 (French, with French summary). Séminaire Bourbaki, Vol. 1998/99. MR 1772675
  • 2. P. Deligne, Les constantes des équations fonctionnelles des fonctions 𝐿, Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Springer, Berlin, 1973, pp. 501–597. Lecture Notes in Math., Vol. 349 (French). MR 0349635
  • 3. M. Harris, On the local Langlands correspondence. To appear in Proc. of the Beijing ICM, 2002. Also available at
  • 4. Guy Henniart, Caractérisation de la correspondance de Langlands locale par les facteurs 𝜀 de paires, Invent. Math. 113 (1993), no. 2, 339–350 (French, with English and French summaries). MR 1228128,
  • 5. Guy Henniart, Une preuve simple des conjectures de Langlands pour 𝐺𝐿(𝑛) sur un corps 𝑝-adique, Invent. Math. 139 (2000), no. 2, 439–455 (French, with English summary). MR 1738446,
  • 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).
  • 7. Guy Henniart, Sur la conjecture de Langlands locale pour 𝐺𝐿_{𝑛}, J. Théor. Nombres Bordeaux 13 (2001), no. 1, 167–187 (French, with English and French summaries). 21st Journées Arithmétiques (Rome, 2001). MR 1838079
  • 8. H. Jacquet, I. I. Piatetskii-Shapiro, and J. A. Shalika, Rankin-Selberg convolutions, Amer. J. Math. 105 (1983), no. 2, 367–464. MR 701565,
  • 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. II. On irreducible representations of 𝔊𝔏(𝔫), Ann. Sci. École Norm. Sup. (4) 13 (1980), no. 2, 165–210. MR 584084

Review Information:

Reviewer: Alan Roche
Affiliation: University of Oklahoma
Journal: Bull. Amer. Math. Soc. 40 (2003), 239-246
Published electronically: February 12, 2003
Review copyright: © Copyright 2003 American Mathematical Society