Remark: Family 040. Bloch's conjecture for complex surfaces

Proves Bloch's conjecture: for every smooth connected projective complex surface $S$ with $p_g(S)=0$, the Albanese map ${\mathrm{CH}}_0(S{)}^0\to \mathrm{Alb}(S)(\mathbb{C})$ on integral degree-zero zero-cycles is an isomorphism. This combines the new $p_g=q=0$ theorem with the classical theorem of Bloch, Kas, and Lieberman.

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.