Denominators of Eisenstein cohomology classes for \(\text{GL}_2\) over imaginary quadratic fields
type: Item
instance of: scholarly article
title: Denominators of Eisenstein cohomology classes for \(\text{GL}_2\) over imaginary quadratic fields
zbMATH Open document ID: 1182.11024
author: Tobias Berger
published in: Manuscripta Mathematica
publication date: 2009-02-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0606531
review text: G. Harder initiated a program to describe the cohomology of arithmetic groups in terms of cusp forms and Eisenstein series. Following this program, the author studies the arithmetic of Eisenstein cohomology classes for symmetric spaces associated to \(\text{GL}_2\) over imaginary quadratic fields. In particular, he proves a lower bound for the denominator of degree \(1\) Eisenstein classes in terms of a special \(L\)-value of a Hecke character, as conjectured by Harder. He also provides conditions under which the restriction of the Eisenstein classes to the boundary of the Borel-Serre compactification of the symmetric space is integral.
Mathematics Subject Classification ID: 11F75
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 22E41
zbMATH DE Number: 5520077
zbMATH Keywords: arithmetic groups
zbMATH Keywords: Eisenstein cohomology classes
reviewed by: Pham Huu Tiep
MaRDI profile type: Publication
OpenAlex ID: W2005464332
arXiv ID: math/0606531
cites work: Anticyclotomic main conjectures for CM modular forms
cites work: Corners and arithmetic groups (Appendice: Arrondissement des varietes a coins par A. Douady et L. Herault)
cites work: Q3885948
cites work: Q3125206
cites work: On some results of Atkin and Lehner
cites work: Congruences between Bernoulli-Hurwitz numbers in the supersingular case
cites work: Q3828097
cites work: Denominator of the Eisenstein cohomology of GL\((2)\) over imaginary quadratic fields
cites work: Divisibility of anticyclotomic \(L\)-functions and theta functions with complex multiplication
cites work: A decomposition of spaces of automorphic forms, and the Eisenstein cohomology of arithmetic groups
cites work: On the functional equation of the Artin L-function for characters of real representations
cites work: Q3822262
cites work: Q5557005
cites work: On the Birch and Swinnerton-Dyer conjecture
cites work: On the critical values of Hecke \(L\)-functions for imaginary quadratic fields
cites work: Q5427834
cites work: Eisenstein cohomology of arithmetic groups. The case \(GL_ 2\)
cites work: Eisenstein cohomology and the construction of mixed motives
cites work: Modular konstruierte unverzweigte abelsche p-Erweiterungen von Q(ζp) und die Struktur ihrer Galoisgruppen
cites work: Automorphic forms on semisimple Lie groups. Notes by J. G. M. Mars.
cites work: Q4695321
cites work: Q3154991
cites work: On the anticyclotomic main conjecture for CM fields
cites work: \(p\)-adic interpolation of real analytic Eisenstein series
cites work: \(p\)-adic \(L\)-functions for CM fields
cites work: Q3348000
cites work: Q5612629
cites work: On the functional equations satisfied by Eisenstein series
cites work: Modular symbols and values of L-functions on GL3
cites work: Eisenstein cohomology and the construction of \(p\)-adic analytic \(L\)-functions
cites work: A modular construction of unramified p-extensions of \(\mathbb{Q}(\mu_p)\)
cites work: Root Numbers of Hecke L-Functions of CM Fields
cites work: Congruences for special values of L-functions of elliptic curves with complex multiplication
cites work: Q4702590
cites work: Kohomologie arithmetisch definierter Gruppen und Eisensteinreihen
cites work: \(l\)-adic representations associated to modular forms over imaginary quadratic fields. II
cites work: On the anticyclotomic main conjecture
cites work: Q4863731
cites work: Congruence module for \(\text{GL}(2)\) of an imaginary quadratic field and Iwasawa theory of biquadratic CM field
cites work: Q3682555
cites work: Eisensteinkohomologie und Dedekindsummen für GL2 über imaginär-quadratischen Körpern.
cites work: On CM Abelian varieties over imaginary quadratic fields
cites work: Q1808887
DOI: 10.1007/S00229-007-0139-6
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description: scientific article