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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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PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 29 July 2021

Introduction

Introduction

Chapter:
(p.1) Chapter One Introduction
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/9780691197890.003.0001

This introductory chapter presents the general principle that the cohomology of arithmetic groups and the L-functions L(s, π‎, r) attached to irreducible “pieces” π‎ have a strong symbiotic relationship with each other. The symbiosis goes in both directions. The first is that expressions in the special values L(k, π‎, r) enter in the transcendental description of the cohomology. Since the cohomology is defined over ℚ one can deduce rationality (algebraicity) results for these expressions in special values. Next, these special values in turn influence the structure of the cohomology as a Hecke module; prime numbers dividing these values occur in the denominators of Eisenstein classes.

Keywords:   cohomology, arithmetic groups, L-functions, symbiosis, algebraicity, Eisenstein cohomology, Eisenstein classes

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