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

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(χ,0) for Hecke characters χ of arbitrary totally imaginary fields, can be regarded as de Rham classes of Blasius' reflex motive.