{"id":"openai-math/Weil-classes-and-Hodge-classes-on-abelian-powers","pdf":"https://github.com/openai/math/blob/main/preprints/Weil-classes-and-Hodge-classes-on-abelian-powers-October-6-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Weil-classes-and-Hodge-classes-on-abelian-powers-October-6-2026","tags":["hodge-theory","abelian-varieties","algebraic-cycles"],"score":0,"title":"Weil classes and Hodge classes on abelian powers","domain":"Algebraic and complex geometry","family":"032","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We prove the rational Hodge conjecture in every codimension on every self-power of a complex abelian sixfold with an imaginary-quadratic action and a compatible polarization whose rational homological Hermitian form is hyperbolic of signature $`(3,3)`$. We also prove it in every codimension on every self-power of a complex abelian variety of dimension at most five admitting an imaginary-quadratic action. Both results include nonsimple varieties and special periods with additional endomorphisms. The proof uses the companion theorem on the rational Hodge conjecture for CM abelian varieties.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-06","reactions":{},"formalized":false,"family_title":"The rational Hodge conjecture for CM abelian varieties"}