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Cohomology of Drinfeld modular varie...

Laumon, Gerard.

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Cohomology of Drinfeld modular varieties.. Part 2,. Automorphic forms, trace formulas, and Langlands correspondence

Record Type:	Electronic resources : Monograph/item
Title/Author:	Cohomology of Drinfeld modular varieties./ Gerard Laumon ; appendix by Jean Loup Waldspurger.
Author:	Laumon, Gerard.
Published:	Cambridge :Cambridge University Press, : 1997.,
Description:	xi, 366 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 31 May 2016).
Subject:	Drinfeld modular varieties. -
Online resource:	https://doi.org/10.1017/CBO9780511661969
ISBN:	9780511661969

Cohomology of Drinfeld modular varieties.. Part 2,. Automorphic forms, trace formulas, and Langlands correspondence
Laumon, Gerard.

Cohomology of Drinfeld modular varieties.Part 2,Automorphic forms, trace formulas, and Langlands correspondence[electronic resource] /Gerard Laumon ; appendix by Jean Loup Waldspurger. - Cambridge :Cambridge University Press,1997. - xi, 366 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;56. - Cambridge studies in advanced mathematics ;56..

Title from publisher's bibliographic system (viewed on 31 May 2016).

Cohomology of Drinfeld Modular Varieties provides 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. This second volume is concerned with the Arthur-Selberg trace formula, and with the proof in some cases of the Rmamanujan-Petersson conjecture and the global Langlands conjecture for function fields. 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.

ISBN: 9780511661969Subjects--Topical Terms:

708476
Drinfeld modular varieties.

LC Class. No.: QA251 / .L287 1997

Dewey Class. No.: 512.24

Cohomology of Drinfeld modular varieties.. Part 2,. Automorphic forms, trace formulas, and Langlands correspondence
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520 $a Cohomology of Drinfeld Modular Varieties provides 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. This second volume is concerned with the Arthur-Selberg trace formula, and with the proof in some cases of the Rmamanujan-Petersson conjecture and the global Langlands conjecture for function fields. 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.
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