Deligne's conjecture on the critical values of Hecke $L$-functions

Abstract

In this paper we give a proof of Deligne's conjecture on the critical values of $L$-functions for arbitrary algebraic Hecke characters. This extends a result of Blasius, which only works in the case of CM fields. The key new insight is that the Eisenstein-Kronecker classes of Kings-Sprang, which allow for a cohomological interpretation of the value $L(\chi,0)$ for Hecke characters $\chi$ of arbitrary totally imaginary fields, can be regarded as de Rham classes of Blasius' reflex motive.