Algebraic and complex geometry·OpenAI Math·Result 040
Bloch’s conjecture for complex surfaces
One of the 372 results in OpenAI's public mathematics catalogue, filed under algebraic and complex geometry: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
Bloch’s conjecture for surfaces with pg=0
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What OpenAI claims
Proves Bloch's conjecture: for every smooth connected projective complex surface S with pg(S)=0, the Albanese map CH0(S)0 → Alb(S)(ℂ) on integral degree-zero zero-cycles is an isomorphism. This combines the new pg=q=0 theorem with the classical theorem of Bloch, Kas, and Lieberman.
Paper
Bloch’s conjecture for surfaces with pg=0
We prove Bloch's conjecture for smooth connected projective complex surfaces with pg=0: the Albanese homomorphism on integral degree-zero zero-cycles is an isomorphism.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
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