Hodge classes on abelian varieties

Abstract

We prove, following Deligne and André, 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, André, ...).

5 pages. No new results, but the proofs are shorter. v2 exposition improved

Cited by in corpus (1)

• Grothendieck's standard conjecture of Lefschetz type over finite fields