Eisenstein cohomology classes for GL<sub> <i>N</i> </sub> over imaginary quadratic fields-Reference-Cited by-同舟云学术

Eisenstein cohomology classes for GL_N over imaginary quadratic fields

Published:2023-03-04 Issue:0 Volume:0 Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Bergeron Nicolas¹,Charollois Pierre²,García Luis E.³

Affiliation:

1. Département de Mathématiques et Applications , ENS / PSL University , 75005 , Paris , France

2. Sorbonne Université and Université Paris Cité , CNRS, IMJ-PRG, F-75005 Paris , France

3. Department of Mathematics , University College London , Gower Street , London WC1E 6BT , United Kingdom

Abstract

Abstract We study the arithmetic of degree N - 1

{N-1}

Eisenstein cohomology classes for the locally symmetric spaces attached to GL N

{\mathrm{GL}_{N}}

over an imaginary quadratic field k. Under natural conditions we evaluate these classes on ( N - 1 )

{(N-1)}

-cycles associated to degree N extensions L / k

{L/k}

as linear combinations of generalized Dedekind sums. As a consequence we prove a remarkable conjecture of Sczech and Colmez expressing critical values of L-functions attached to Hecke characters of L as polynomials in Kronecker–Eisenstein series evaluated at torsion points on elliptic curves with complex multiplication by k. We recover in particular the algebraicity of these critical values.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2022-0089/pdf

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