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Book Review

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MathSciNet review: 2798318
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Book Information:

Author: 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., ISBN 978-0-691-12330-1, $59.50$, paper
$99.50 (cloth), ISBN 13: 978-0-691-12329-5$

A. A. Beĭlinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces, I (Luminy, 1981) Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171 (French). MR 751966
Pierre Deligne, La conjecture de Weil. II, Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137–252 (French). MR 601520
Mark Goresky and Robert MacPherson, Intersection homology theory, Topology 19 (1980), no. 2, 135–162. MR 572580, DOI https://doi.org/10.1016/0040-9383%2880%2990003-8
Robert M. Guralnick and Pham Huu Tiep, Decompositions of small tensor powers and Larsen’s conjecture, Represent. Theory 9 (2005), 138–208. MR 2123127, DOI https://doi.org/10.1090/S1088-4165-05-00192-5

Clozel, Laurent; Harris, Michael; Taylor, Richard: Automorphy for some $\ell$ -adic lifts of automorphic mod $\ell$ representations, preprint.

Harris, Michael; Shepherd-Barron, Nicholas; Taylor, Richard: A family of Calabi-Yau varieties and potential automorphy, preprint.

Taylor, Richard: Automorphy for some $\ell$ -adic lifts of automorphic mod $\ell$ representations, II, preprint.

Nicholas M. Katz, Sommes exponentielles, Astérisque, vol. 79, Société Mathématique de France, Paris, 1980 (French). 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. MR 617009
Nicholas M. Katz, Gauss sums, Kloosterman sums, and monodromy groups, Annals of Mathematics Studies, vol. 116, Princeton University Press, Princeton, NJ, 1988. MR 955052
Nicholas M. Katz, Exponential sums and differential equations, Annals of Mathematics Studies, vol. 124, Princeton University Press, Princeton, NJ, 1990. MR 1081536
Nicholas M. Katz, Twisted $L$-functions and monodromy, Annals of Mathematics Studies, vol. 150, Princeton University Press, Princeton, NJ, 2002. MR 1875130
M. Larsen and R. Pink, Determining representations from invariant dimensions, Invent. Math. 102 (1990), no. 2, 377–398. MR 1074479, DOI https://doi.org/10.1007/BF01233432
Hermann Weyl, The classical groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Their invariants and representations; Fifteenth printing; Princeton Paperbacks. MR 1488158

Review Information:

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

Journal: Bull. Amer. Math. Soc. 46 (2009), 137-141
DOI: https://doi.org/10.1090/S0273-0979-08-01203-2
Published electronically: September 15, 2008
Review copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.