Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions [electronic resource] / Günter Harder, A. Raghuram.
- 作者： Harder, Günter, 1938-
- 其他作者：
- 出版： Princeton, NJ : Princeton University Press c2020.
- 叢書名： Annals of mathematics studies ;203
- 主題： Shimura varieties. , Cohomology operations. , Number theory. , Arithmetic groups. , L-functions.
- ISBN： 9780691197937 (pdf)
- URL：
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- 一般註：Includes bibliographical references and index. 111年度臺灣學術電子書暨資料庫聯盟採購
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讀者標籤：
- 系統號： 000299341 | 機讀編目格式
館藏資訊
This book studies the interplay between the geometry and topology of locally symmetric spaces, and the arithmetic aspects of the special values of L-functions. The authors study the cohomology of locally symmetric spaces for GL(N) where the cohomology groups are with coefficients in a local system attached to a finite-dimensional algebraic representation of GL(N). The image of the global cohomology in the cohomology of the Borel–Serre boundary is called Eisenstein cohomology, since at a transcendental level the cohomology classes may be described in terms of Eisenstein series and induced representations. However, because the groups are sheaf-theoretically defined, one can control their rationality and even integrality properties. A celebrated theorem by Langlands describes the constant term of an Eisenstein series in terms of automorphic L-functions. A cohomological interpretation of this theorem in terms of maps in Eisenstein cohomology allows the authors to study the rationality properties of the special values of Rankin–Selberg L-functions for GL(n) x GL(m), where n + m = N. The authors carry through the entire program with an eye toward generalizations. This book should be of interest to advanced graduate students and researchers interested in number theory, automorphic forms, representation theory, and the cohomology of arithmetic groups.
摘要註
"This monograph, which is intended for the Annals of Math Studies, presents an important new result that lies at the intersection of number theory, geometry, and representation theory. Accordingly, the book will serve as a key reference in these fields. Given its comprehensive methodological approach, the book will also provide a model for future work in these areas. This monograph builds on over forty years of ambitious research, initiated by Günter Harder in 1975. The results presented in this book extend well beyond previous research in the field, and are readily generalizeable"--