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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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The Strongly Inner Spectrum and Applications

The Strongly Inner Spectrum and Applications

Chapter:
(p.51) Chapter Five The Strongly Inner Spectrum and Applications
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/9780691197890.003.0005

This chapter turns to the strongly inner spectrum. It first defines the strongly inner spectrum and its properties. Next, the chapter gives the definition of relative periods. It considers the group G = RF/ℚ(GLn/F) only when n is an even positive integer. The chapter then defines and analyzes certain relative periods Ω‎ε‎(ι‎π‎f) ∈ ℂ×, where λ‎ = (λ‎τ‎)τ‎:FE is a pure weight, π‎f ∈ Coh!!(G, Kf, λ‎) for some level structure Kf, ι‎ : E → ℂ, and ε‎ = (ε‎ν‎)ν‎∈S is a character of π‎0(G(ℝ)). Finally, the chapter demonstrates the strongly inner cohomology of the boundary. It presents some interludes on Kostant's representatives, on induced representations, and on arithmetic identifications.

Keywords:   strongly inner spectrum, relative periods, strongly inner cohomology, Kostant's representatives, induced representations, arithmetic identifications

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