${\mathbb{A}}^1$-equivalence of zero cycles on surfaces

Abstract

In this paper, we study ${\mathbb{A}}^1$-equivalence classes of zero cycles on open complex algebraic surfaces. We prove the logarithmic version of Mumford's theorem on zero cycles and prove that log Bloch's conjecture holds for quasiprojective surfaces with log Kodaira dimension $-\infty$.

arXiv comment17 pages. Final version