Milne's rationality conjecture for abelian varieties
Source: github.com/openai/math/tree/main/preprints/Milnes-rationali…
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.
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Notes & Talks | Keerthi Madapusikeerthimadapusi.comKeerthi Madapusi
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…