Bloch's Conjecture for Surfaces with $p_g=0$

For every smooth connected projective complex surface $S$ with $p_g=q=0$, $\deg:\mathrm{CH}_0(S)\to\mathbb{Z}$ is an isomorphism with integral coefficients, with no minimality, fundamental-group or construction hypothesis. With Bloch-Kas-Lieberman this gives $\mathrm{CH}_0(S)^0\cong\mathrm{Alb}(S)(\mathbb{C})$ for every such surface with $p_g=0$. Over $\mathbb{C}$ only; it does not address the generalized Bloch conjecture in higher dimension. An earlier proof of the same statement was proposed by Guletskii (arXiv:2512.12451, December 2025), which the manuscript cites; this entry claims no priority over it.

For every smooth connected projective complex surface $S$ with $p_g=q=0$, $\deg:\mathrm{CH}_0(S)\to\mathbb{Z}$ is an isomorphism with integral coefficients, with no minimality, fundamental-group or construction hypothesis. With Bloch-Kas-Lieberman this gives $\mathrm{CH}_0(S)^0\cong\mathrm{Alb}(S)(\mathbb{C})$ for every such surface with $p_g=0$. Over $\mathbb{C}$ only; it does not address the generalized Bloch conjecture in higher dimension. An earlier proof of the same statement was proposed by Guletskii (arXiv:2512.12451, December 2025), which the manuscript cites; this entry claims no priority over it.