Eisenstein Cohomology for GLN and the Special Values of Rankin–Selberg L-Functions: (AMS-203)

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Günter Harder Anantharam Raghuram

Eisenstein Cohomology for GLN and the Special Values of Rankin–Selberg L-Functions

AMS-203

Günter Harder, Anantharam Raghuram

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English

Princeton University Press
03 December 2019

Number theory; Algebraic geometry

Series: Annals of Mathematics Studies

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.

By: Günter Harder, Anantharam Raghuram
Imprint: Princeton University Press
Country of Publication: United States
Volume: 370
Dimensions: Height: 235mm, Width: 156mm,
ISBN: 9780691197890
ISBN 10: 069119789X
Series: Annals of Mathematics Studies
Pages: 240
Publication Date: 03 December 2019
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

Gnter Harder is professor emeritus of mathematics at the University of Bonn and former director of the Max Planck Institute for Mathematics. He is the author of the two-volume Lectures on Algebraic Geometry. A. Raghuram is professor and chair of mathematics at the Indian Institute of Science Education and Research, Pune.