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

Boundary Cohomology

Chapter:
(p.40) Chapter Four Boundary 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/9780691197890.003.0004

This chapter discusses some relevant details of the cohomology of the boundary of the Borel–Serre compactification of the locally symmetric space SGKf. It first illustrates a spectral sequence converging to boundary cohomology. The chapter then turns to the cohomology of PSG to better understand the cohomology of the boundary. Finally, the chapter describes the contribution of the discrete but noncuspidal spectrum to cohomology. It formulates the consequences of the description of the discrete spectrum in Mœglin–Waldspurger for the square integrable cohomology. In a sense, the chapter makes their results more explicit. It works at a transcendental level: the coefficient systems are ℂ-vector spaces.

Keywords:   boundary cohomology, Borel–Serre compactification, locally symmetric space, discrete spectrum, Mœglin–Waldspurger, square integrable cohomology

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