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

Anantharam Raghuram and Günter Harder

Print publication date: 2019

Print ISBN-13: 9780691197890

Published to Princeton Scholarship Online: September 2020

DOI: 10.23943/princeton/9780691197890.001.0001

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Eisenstein Cohomology

Eisenstein Cohomology

Chapter:
(p.71) Chapter Six Eisenstein Cohomology
Source:
Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions
Author(s):

Günter Harder

A. Raghuram

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691197890.003.0006

This chapter provides the Eisenstein cohomology. It begins with the Poincaré duality and maximal isotropic subspace of boundary cohomology. Here, the chapter considers the compatibility of duality isomorphisms with the connecting homomorphism. It then states and proves the main result on rank-one Eisenstein cohomology. Thereafter, the chapter presents a theorem of Langlands: the constant term of an Eisenstein series. It draws some details from the Langlands–Shahidi method in this context. Induced representations are examined, as are standard intertwining operators. The chapter finally illustrates the Eisenstein series, the constant term of an Eisenstein series, and the holomorphy of the Eisenstein series at the point of evaluation.

Keywords:   Eisenstein cohomology, boundary cohomology, Poincaré duality, duality isomorphisms, connecting homomorphism, Langlands–Shahidi method, induced representations, standard intertwining operators, Eisenstein series

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