Eisenstein cocycles for GL(n) and values of L-functions in imaginary quadratic extensions

TL;DR

This paper extends Eisenstein cocycles to imaginary quadratic fields, providing a cohomological framework to interpret special values of Hecke L-functions and their algebraicity properties.

Contribution

It generalizes Eisenstein cocycles for GL(n) to imaginary quadratic extensions, linking them to special L-values and algebraicity results.

Findings

Cohomological interpretation of Hecke L-values

Extension of Eisenstein cocycles to imaginary quadratic fields

Parametrization of special L-values via cocycles

Abstract

We generalize Sczech's Eisenstein cocycle for $\mathrm{GL}(n)$ over totally real extensions of $\mathbb{Q}$ to finite extensions of imaginary quadratic fields. By evaluating the cocycle on certain cycles, we parametrize complex values of Hecke L-functions previously considered by Colmez, giving a cohomological interpretation of his algebraicity result on special values of the L-functions.