Family 040Algebraic and complex geometryNo LeanNot yet digested

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.

Manuscripts in this family · 1

Sep 24, 2026·paper.pdf

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.

Full abstract