A remark on the Tate conjecture
Algebraic Geometry
2018-03-20 v2 Number Theory
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.
Keywords
Cite
@article{arxiv.1709.04489,
title = {A remark on the Tate conjecture},
author = {Ben Moonen},
journal= {arXiv preprint arXiv:1709.04489},
year = {2018}
}
Comments
3 pages; updated version that includes a result in characteristic p. To appear in the J. of Alg. Geom