Geometry and topology · Oct 6, 2026
Rational Hodge 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.
Scope and what remains
Not the complete Hodge conjecture. Three related manuscripts were withdrawn October 7 and must remain separate, invalidated arguments.
Contributors
OpenAI source publisher and an unnamed unreleased internal model. Exact paper-level human roles are not disclosed by the family summary.
AI systems: Unreleased OpenAI model