A remark on the Tate conjecture

2017/09/13 by Moonen, Ben
#14C15 #14C25 #14F20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1709.04489

Abstract

The Tate conjecture has two parts: an assertion (S) about semisimplicity of Galois representations, and an assertion (T) which says that every Tate class is algebraic. We show that in characteristic 0, (T) implies (S). In characteristic p an analogous result is true under stronger assumptions.

Related

• On the observability of Galois representations and the Tate conjecture
• Building bridges between Tate conjectures and arithmetic invariants
• Variations on a theorem of Tate
• Arithmetic Duality
• The Mumford-Tate conjecture implies the algebraic Sato-Tate conjecture of Banaszak and Kedlaya