Geometry and topology · Oct 6, 2026

Bloch’s conjecture for complex surfaces

Proves Bloch's conjecture: for every smooth connected projective complex surface S with pg(S)=0p_g(S)=0, the Albanese map CH0(S)0→Alb(S)(C)\mathrm{CH}_0(S)^0\to\mathrm{Alb}(S)(\mathbb C) on integral degree-zero zero-cycles is an isomorphism. This combines the new pg=q=0p_g=q=0 theorem with the classical theorem of Bloch, Kas, and Lieberman.

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