Eisenstein Cohomology Classes For GLN Over Imaginary Quadratic Fields
Résumé
We study the arithmetic of degree N − 1 Eisenstein cohomology classes for the locally symmetric spaces attached to GLN over an imaginary quadratic field k. Under natural conditions we evaluate these classes on (N −1)-cycles associated to degree N extensions L/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.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)