{"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":1,"published":"2026-10-07","reactions":{},"discussion":[{"url":"https://keerthimadapusi.com/notes#:~:text=The%20first%20proof%20in%20the%20OpenAI%20dump%20on%20Oct%206%2C%202026%20was%20a%20proof%20of%20a%20rationality%20conjecture%20of%20Milne","kind":"web","site":"keerthimadapusi.com","text":"The first proof in the OpenAI dump on Oct 6, 2026 was a proof of a rationality conjecture of Milne. Its organization and exposition were characteristically incomprehensible, but the underlying idea turns out to be quite simple and quite clever, as I discovered after waterboarding Astra 6 into…","added":"2026-11-03","title":"Notes & Talks | Keerthi Madapusi","author":"Keerthi Madapusi"}],"formalized":false,"family_title":"Milne’s rationality conjecture and algebraic specialization"}