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Weil classes and Hodge classes on abelian powers

OpenAI · September 30, 2026

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This is an earlier edition (September 30, 2026). Current edition: Weil classes and Hodge classes on abelian powers, October 6, 2026.

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@misc{OAI:Weil-classes-and-Hodge-classes-on-abelian-powers-September-30-2026,
  author = {{OpenAI}},
  title = {{Weil classes and Hodge classes on abelian powers}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Weil-classes-and-Hodge-classes-on-abelian-powers-September-30-2026/paper.pdf}{OAI:Weil-classes-and-Hodge-classes-on-abelian-powers-September-30-2026}},
  year = {2026}
}

Family 032: The rational Hodge conjecture for CM abelian varieties

Proves the rational Hodge conjecture for every complex CM abelian variety, in every dimension and codimension. Through Milne's theorems, this also gives the Tate conjecture for all abelian varieties over finite fields and the Hodge standard conjecture for abelian varieties in every characteristic.

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