Hodge classes on abelian varieties
Algebraic Geometry
2020-11-13 v2 Number Theory
Abstract
We prove, following Deligne and Andr\'e, that the Hodge classes on abelian varieties of CM-type can be expressed in terms of divisor classes and split Weil classes, and we describe some consequences. In particular, we show that Grothendieck's standard conjecture of Lefschetz type implies the Hodge conjecture for abelian varieties (Abdulali, Andr\'e, ...).
Keywords
Cite
@article{arxiv.2010.08857,
title = {Hodge classes on abelian varieties},
author = {James S. Milne},
journal= {arXiv preprint arXiv:2010.08857},
year = {2020}
}
Comments
5 pages. No new results, but the proofs are shorter. v2 exposition improved