Eisenstein cohomology of arithmetic groups. The case GL2

1987 ◽  
Vol 89 (1) ◽  
pp. 37-118 ◽  
Author(s):  
G. Harder
Keyword(s):  
Arithmetic Groups ◽  
Cohomology Of Arithmetic Groups ◽  
Eisenstein Cohomology

On the Eisenstein cohomology of arithmetic groups

2004 ◽  
Vol 123 (1) ◽  
pp. 141-169 ◽  
Author(s):  
Jian-Shu Li ◽  
Joachim Schwermer
Keyword(s):  
Arithmetic Groups ◽  
Cohomology Of Arithmetic Groups ◽  
Eisenstein Cohomology

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

2019 ◽  
Author(s):  
Anantharam Raghuram ◽  
Günter Harder
Keyword(s):  
Eisenstein Series ◽  
Symmetric Spaces ◽  
Constant Term ◽  
Local System ◽  
Arithmetic Groups ◽  
Special Values ◽  
Cohomology Of Arithmetic Groups ◽  
Finite Dimensional ◽  
Eisenstein Cohomology ◽  
Cohomological Interpretation

This book studies 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) × GL(m), where n + m = N. The book carries through the entire program with an eye toward generalizations. The 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.

Introduction to the Schwartz Space of T\G

1989 ◽  
Vol 41 (2) ◽  
pp. 285-320 ◽  
Author(s):  
W. Casselman
Keyword(s):  
Reductive Group ◽  
Rational Points ◽  
Schwartz Space ◽  
Parabolic Subgroups ◽  
Arithmetic Groups ◽  
Similar Question ◽  
Arithmetic Subgroup ◽  
Cohomology Of Arithmetic Groups ◽  
Image Position

Let G be the group of R-rational points on a reductive group defined over Q and T an arithmetic subgroup. The aim of this paper is to describe in some detail the Schwartz space (whose definition I recall in Section 1) and in particular to explain a decomposition of this space into constituents parametrized by the T-associate classes of rational parabolic subgroups of G. This is analogous to the more elementary of the two well known decompositions of L2 (T\G) in [20](or [17]), and a proof of something equivalent was first sketched by Langlands himself in correspondence with A. Borel in 1972. (Borel has given an account of this in [8].)Langlands’ letter was in response to a question posed by Borel concerning a decomposition of the cohomology of arithmetic groups, and the decomposition I obtain here was motivated by a similar question, which is dealt with at the end of the paper.

Mini-Workshop: Computations in the Cohomology of Arithmetic Groups

2017 ◽  
Vol 13 (4) ◽  
pp. 2941-2973
Author(s):  
Eva Bayer-Fluckiger ◽  
Philippe Elbaz-Vincent ◽  
Graham Ellis
Keyword(s):  
Arithmetic Groups ◽  
Cohomology Of Arithmetic Groups

On Eisenstein series and the cohomology of arithmetic groups

2010 ◽  
Vol 348 (11-12) ◽  
pp. 597-600 ◽  
Author(s):  
Neven Grbac ◽  
Joachim Schwermer
Keyword(s):  
Eisenstein Series ◽  
Arithmetic Groups ◽  
Cohomology Of Arithmetic Groups
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