Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points a

Description: Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis by Gerard Laumon This 1995 book introduces the reader to Drinfeld modular varieties, and is pitched at graduate students. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description Cohomology of Drinfeld Modular Varieties aims to provide an introduction, in two volumes, both to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fields of the Shimura varieties over number fields. The Langlands correspondence is a conjectured link between automorphic forms and Galois representations over a global field. By analogy with the number-theoretic case, one expects to establish the conjecture for function fields by studying the cohomology of Drinfeld modular varieties, which has been done by Drinfeld himself for the rank two case. The present volume is devoted to the geometry of these varieties, and to the local harmonic analysis needed to compute their cohomology. It is based on graduate courses taught by the author, who uses techniques which are extensions of those used to study Shimura varieties. Though the author considers only the simpler case of function rather than number fields, many important features of the number field case can be illustrated. Several appendices on background material keep the work reasonably self-contained.It is the first book on this subject and will be of much interest to all researchers in algebraic number theory and representation theory. Table of Contents 1. Construction of Drinfeld modular varieties; 2. Drinfeld A-modules; 3. The Lefschetz numbers of Hecke operators; 4. The fundamental lemma; 5. Very cuspidal Euler-Poincare functions; 6. The Lefschetz numbers as sums of global elliptic orbital integrals; 7. Unramified principal series representations; 8. Euler-Poincare functions as pseudocoefficients of the Steinberg relation; Appendices. Review This is a very impressive achievement. Mathematica Promotional "Headline" This 1995 book introduces the reader to Drinfeld modular varieties, and is pitched at graduate students. Description for Bookstore Originally published in 1995, Cohomology of Drinfeld Modular Varieties provided an introduction, in two volumes, to both the subject of the title and the Langlands correspondence for function fields. It is based on courses given by the author and will be welcomed by workers in number theory and representation theory. Description for Library Originally published in 1995, Cohomology of Drinfeld Modular Varieties provided an introduction, in two volumes, to both the subject of the title and the Langlands correspondence for function fields. It is based on courses given by the author and will be welcomed by workers in number theory and representation theory. Details ISBN0521470609 Author Gerard Laumon Short Title COHOMOLOGY OF DRINFELD MODULAR Publisher Cambridge University Press Series Cambridge Studies in Advanced Mathematics (Hardcover) Language English ISBN-10 0521470609 ISBN-13 9780521470605 Media Book Format Hardcover DEWEY 512.24 Series Number 41 Year 1996 Publication Date 1996-01-31 Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom Pages 360 Edition 0003rd Illustrations black & white illustrations Subtitle Geometry, Counting of Points and Local Harmonic Analysis DOI 10.1604/9780521470605 Audience Professional and Scholarly UK Release Date 1995-12-14 AU Release Date 1995-12-14 NZ Release Date 1995-12-14 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:91372478;

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