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.

Manuscript

Bloch’s conjecture for surfaces with p_g=0

September 24, 2026 · source · cite as \cite{OAI:Blochs-Conjecture-for-Surfaces-with-pg-equals-q-equals-0-September-24-2026}

We prove Bloch's conjecture for smooth connected projective complex surfaces with p_g=0: the Albanese homomorphism on integral degree-zero zero-cycles is an isomorphism.

Result 040 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.