Eisenstein cocycles for imaginary quadratic fields

Abstract

We construct Eisenstein cocycles for arithmetic subgroups of GL_2 of imaginary quadratic fields valued in second K-groups of products of two CM elliptic curves. We use these to construct maps from the first homology groups of Bianchi spaces to corresponding second K-groups of ray class fields and to verify the Eisenstein property of these maps for prime-to-level Hecke operators.

46 pages