Motivic Serre group, algebraic Sato-Tate group and Sato-Tate conjecture
Motivic Serre group, algebraic Sato-Tate group and Sato-Tate conjecture
We make explicit Serre's generalization of the Sato-Tate conjecture for motives, by expressing the construction in terms of fiber functors from the motivic category of absolute Hodge cycles into a suitable category of Hodge structures of odd weight.This extends the case of abelian varietes, which we treated in a previous …