Moments, Monodromy, and Perversity. (AM-159): A Diophantine Perspective. (AM-159)

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Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition into the twenty-first century as Princeton looks forward to publishing the major works of the new millennium. To mark the continued success of the series, all books are again available in paperback. For a ...
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Overview

Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition into the twenty-first century as Princeton looks forward to publishing the major works of the new millennium. To mark the continued success of the series, all books are again available in paperback. For a complete list of titles, please visit the Princeton University Press Web site: pup.princeton.edu. The most recently published volumes include: Green's Function Estimates for Lattice Schrodinger Operators and Applications, by J. Bourgain, On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety, by Mark Green and Phillip Griffiths, Radon Transforms and the Rigidity of the Grassmannians, by Jacques Gasqui and Hubert Goldschmidt, Markov Processes from K. Ito's Perspective, by Daniel W. Stroock, Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation, by Spyridon Kamvissis, Kenneth D. T-R. McLaughlin, and Peter D. Miller, Finite Structures with Few Types, by Gregory Cherlin and Ehud Hrushovski, The Geometry and Cohomology of Some Simple Shimura Varieties, by Michael Harris and Richard Taylor with an appendix by Vladimir G. Berkovich, Twisted L-Functions and Monodromy, by Nicholas M. Katz, Surveys on Surgery Theory: Volume 2. Papers Dedicated to C. T. C. Wall, edited by Sylvain Cappell, Andrew Ranicki, and Jonathan Rosenberg, Triangulated Categories, by Amnon Neeman.
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Product Details

  • ISBN-13: 9780691123295
  • Publisher: Princeton University Press
  • Publication date: 9/12/2005
  • Series: Annals of Mathematics Studies
  • Pages: 448
  • Product dimensions: 7.12 (w) x 10.24 (h) x 1.47 (d)

Meet the Author

Nicholas M. Katz is Professor of Mathematics at Princeton University. He is the author of five previous books in this series: "Arithmetic Moduli of Elliptic Curves" (with Barry Mazur); "Gauss Sums, Kloosterman Sums, and Monodromy Groups"; "Exponential Sums and Differential Equations"; "Rigid Local Systems"; and "Twisted L-Functions and Monodromy".

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Table of Contents

Ch. 1 Basic results on perversity and higher moments 9
Ch. 2 How to apply the results of Chapter 1 93
Ch. 3 Additive chapter sums on A[superscript n] 111
Ch. 4 Additive character sums on more general X 161
Ch. 5 Multiplicative character sums on A[superscript n] 185
Ch. 6 Middle additive convolution 221
App. A6 Swan-minimal poles 281
Ch. 7 Pullbacks to curves from A[superscript 1] 295
Ch. 8 One variable twists on curves 321
Ch. 9 Weierstrass sheaves as inputs 327
Ch. 10 Weierstrass families 349
Ch. 11 FJTwist families and variants 371
Ch. 12 Uniformity results 407
Ch. 13 Average analytic rank and large N limits 443
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