On critical values of L-functions of potentially automorphic motives

TL;DR

This paper proves a version of Deligne's conjecture for potentially automorphic motives twisted by specific algebraic Hecke characters, utilizing automorphic methods on totally definite unitary groups.

Contribution

It introduces a new approach to Deligne's conjecture for potentially automorphic motives using automorphic techniques on unitary groups.

Findings

Established a version of Deligne's conjecture for certain motives.

Demonstrated the effectiveness of automorphic methods in this context.

Extended the understanding of L-functions of automorphic motives.

Abstract

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.