A survey around the Hodge, Tate and Mumford-Tate conjectures for abelian varieties
arXiv:1602.08354
Abstract
This survey describe Hodge, Tate and Mumford-Tate conjectures for abelian varieties. After some preliminaries on endomorphism ring, polarization and algebraic cycles, we state the three conjectures and provide a list of know results. Finally, we explain some links between these conjectures.