Remark: Family 032. The rational Hodge conjecture 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.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.