In this paper we prove a version of Deligne's conjecture for potentially automorphic motives, twisted by certain algebraic Hecke characters. The Hecke characters are chosen in such a way that we can use automorphic methods in the context of totally definite unitary groups.
Barrera, D., Guerberoff, L. On critical values of L-functions of potentially automorphic motives. "Manuscripta mathematica", 1 Juliol 2017, vol. 153, núm. 3-4, p. 341-371.