Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions (Book, 2020) [WorldCat.org]
skip to content
Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions Preview this item
ClosePreview this item
Checking...

Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions

Author: Günter Harder; A Raghuram
Publisher: Princeton, New Jersey : Princeton University Press, 2020 ©2020
Series: Annals of mathematics studies, number 203.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
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  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Additional Physical Format: Online version:
Harder, Günter, 1938-
Eisenstein cohomology for gln and the special values of Rankin-Selberg l-functions
Princeton : Princeton University Press, 2019.
Document Type: Book
All Authors / Contributors: Günter Harder; A Raghuram
ISBN: 9780691197883 0691197881 9780691197890 069119789X
OCLC Number: 1233147461
Description: xi, 220 pages 24 cm.
Contents: Introduction --
The cohomology of GLn --
Analytic tools --
Boundary cohomology --
The strongly inner spectrum and applications --
Eisenstein cohomology --
L-functions --
Harish-Chandra modules over Z / by Günter Harder --
Archimedean intertwining operator / by Uwe Weselmann.
Series Title: Annals of mathematics studies, number 203.
Responsibility: Günter Harder, A. Raghuram.

Abstract:

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.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.