A remark on the Tate conjecture

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.

3 pages; updated version that includes a result in characteristic p. To appear in the J. of Alg. Geom