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ISSN 1088-9485(e) ISSN 0273-0979(p)

Book Review

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Book Information

Author(s): Nicholas M. Katz
Title: Moments, monodromy, and perversity: Diophantine perspective
Additional book information: Annals of Mathematics Studies, 159, Princeton University Press, Princeton, NJ, 2005, viii+475 pp., (paper) $59.50, ISBN 978-0-691-12330-1
$99.50 (cloth), ISBN 13: 978-0-691-12329-5

References:

1.: Beĭlinson, A. A.; Bernstein, J.; Deligne, P. Faisceaux pervers. Analysis and topology on singular spaces, I (Luminy, 1981), 5-171, Astérisque, 100, Soc. Math. France, Paris, 1982. MR 751966 (86g:32015)
2.: Deligne, Pierre: La conjecture de Weil. II. Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137-252. MR 601520 (83c:14017)
3.: Goresky, Mark; MacPherson, Robert. Intersection homology theory. Topology 19 (1980), no. 2, 135-162. MR 572580 (82b:57010)
4.: Guralnick, Robert M.; Tiep, Pham Huu: Decompositions of small tensor powers and Larsen's conjecture. Represent. Theory 9 (2005), 138-208. MR 2123127 (2006a:20082)
5.: Clozel, Laurent; Harris, Michael; Taylor, Richard: Automorphy for some $\ell$ -adic lifts of automorphic mod $\ell$ representations, preprint.
6.: Harris, Michael; Shepherd-Barron, Nicholas; Taylor, Richard: A family of Calabi-Yau varieties and potential automorphy, preprint.
7.: Taylor, Richard: Automorphy for some $\ell$ -adic lifts of automorphic mod $\ell$ representations, II, preprint.
8.: Katz, Nicholas M.: Sommes exponentielles. Course taught at the University of Paris, Orsay, Fall 1979. With a preface by Luc Illusie. Notes written by Gérard Laumon. With an English summary. Astérisque, 79. Société Mathématique de France, Paris, 1980. MR 617009 (82m:10059)
9.: Katz, Nicholas M.: Gauss sums, Kloosterman sums, and monodromy groups. Annals of Mathematics Studies, 116. Princeton University Press, Princeton, NJ, 1988. MR 955052 (91a:11028)
10.: Katz, Nicholas M.: Exponential sums and differential equations. Annals of Mathematics Studies, 124. Princeton University Press, Princeton, NJ, 1990. MR 1081536 (93a:14009)
11.: Katz, Nicholas M.: Twisted -functions and monodromy. Annals of Mathematics Studies, 150. Princeton University Press, Princeton, NJ, 2002. MR 1875130 (2003i:11087)
12.: Larsen, M.; Pink, R.: Determining representations from invariant dimensions. Invent. Math. 102 (1990), no. 2, 377-398. MR 1074479 (92c:22026)
13.: Weyl, Hermann: The Classical Groups. Their Invariants and Representations. Princeton University Press, Princeton, N.J., 1939. MR 1488158 (98k:01049)

Additional Information:

Reviewer(s):
Michael Larsen
Affiliation: Indiana University
Email: larsen@math.indiana.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 46 (2009), 137-141.

MSC (2000): Primary 14F20; Secondary 11G05, 11T23, 14G10, 14G15
DOI: 10.1090/S0273-0979-08-01203-2
PII: S 0273-0979(08)01203-2
Posted: September 15, 2008
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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