{"id":"openai-math/Milnes-rationality-conjecture-for-abelian-varieties","pdf":"https://github.com/openai/math/blob/main/preprints/Milnes-rationality-conjecture-for-abelian-varieties-October-7-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Milnes-rationality-conjecture-for-abelian-varieties-October-7-2026","tags":["algebraic-geometry","hodge-theory","abelian-varieties"],"score":0,"title":"Milne's rationality conjecture for abelian varieties","domain":"Number theory","family":"001","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"We prove Milne's rationality conjecture for abelian varieties, including residue characteristic 2. After good reduction, the pairing of a rational Hodge class with any complementary product of divisor classes on the reduction is the same rational number in every prime-to- p realization and in crystalline cohomology. Using the Hodge theorem for CM abelian varieties, we also show that every such specialized Hodge class is represented by a single rational algebraic cycle in all these realizations.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-07","reactions":{},"formalized":false,"family_title":"Milne’s rationality conjecture and algebraic specialization"}