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arXiv · 2010.08857

Hodge classes on abelian varieties

James S. Milne
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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, ...).

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James S. Milne. 2020-10-17. Hodge classes on abelian varieties. https://arxiv.org/abs/2010.08857

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