Eisenstein cohomology classes for $\mathrm{GL}_N$ over imaginary quadratic fields - Département des mathématiques et applications de l'ENS PARIS Accéder directement au contenu
Article Dans Une Revue Journal für die reine und angewandte Mathematik Année : 2023

Eisenstein cohomology classes for $\mathrm{GL}_N$ over imaginary quadratic fields

Pierre Charollois
  • Fonction : Auteur
Luis García
  • Fonction : Auteur

Résumé

We study the arithmetic of degree $N-1$ Eisenstein cohomology classes for locally symmetric spaces associated to $\mathrm{GL}_N$ over an imaginary quadratic field $k$. Under natural conditions we evaluate these classes on $(N-1)$-cycles associated to degree $N$ extensions $F/k$ as linear combinations of generalised 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 $F$ as polynomials in Kronecker--Eisenstein series evaluated at torsion points on elliptic curves with multiplication by $k$. We recover in particular the algebraicity of these critical values.

Dates et versions

hal-03919490 , version 1 (02-01-2023)

Identifiants

Citer

Nicolas Bergeron, Pierre Charollois, Luis García. Eisenstein cohomology classes for $\mathrm{GL}_N$ over imaginary quadratic fields. Journal für die reine und angewandte Mathematik, 2023, ⟨10.48550/arXiv.2107.01992⟩. ⟨hal-03919490⟩
35 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More