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.
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In Bloch’s conjecture for surfaces with p_g=0, 24 September 2026
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Let S be a smooth connected projective surface over \mathbb C with p_g(S)=q(S)=0. Then
is an isomorphism, where \CH_0(S) has integral coefficients.
In Bloch’s conjecture for surfaces with p_g=0, 24 September 2026
Possible match to OpenAI’s description, selected because it shares the most wording. No review confirming the selection is recorded.
Let S be a smooth connected projective surface over \mathbb C with p_g(S)=0. Then the Albanese homomorphism
is an isomorphism of abelian groups, where \CH_0(S) has integral coefficients.
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Simon Pepin Lehalleur, Posts on the Kuga-Satake algebraicity and Bloch conjecture papers, 7 October 2026. Source
Superficial reading: the Bloch conjecture proof for surfaces with p_g = 0 is substantial progress on cycles on surfaces but not a general codimension-2 insight.
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Why this passage is shown
Theorem 1.1
In Bloch’s conjecture for surfaces with p_g=0, 24 September 2026
Why this passage is shown
Corollary 1.2 (Bloch’s conjecture for surfaces with p_g=0)
In Bloch’s conjecture for surfaces with p_g=0, 24 September 2026
Why this passage is shown
Corollary 1.3 (Motivic consequences)
In Bloch’s conjecture for surfaces with p_g=0, 24 September 2026