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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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Analytic Tools

Analytic Tools

Chapter:
(p.28) Chapter Three Analytic Tools
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/9780691197890.003.0003

This chapter goes to the transcendental level, i.e., take an embedding ι‎ : E → ℂ, and extend the ground field to ℂ. The entirety of this chapter works over ℂ and therefore suppresses the subscript ℂ. It begins with the cuspidal parameters and the representation 𝔻λ‎ at infinity. Next, the chapter defines the square-integrable cohomology as well as the de Rham complex. Finally, cuspidal cohomology is addressed. Here, the chapter looks at the cohomological cuspidal spectrum and the consequence of multiplicity one and strong multiplicity one. It also shows the character of the component group I, before dropping the assumption that we are working over ℂ and go back to our coefficient system 𝓜̃λ‎,E defined over E.

Keywords:   analytic tools, square-integrable cohomology, de Rham complex, cuspidal cohomology, cuspidal parameters, multiplicity one, strong multiplicity one

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