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

Abstract

Using recent developments in the theory of mixed motives, we prove that the log Bloch conjecture holds for an open smooth complex surface if the Bloch conjecture holds for its compactification. This verifies the log Bloch conjecture for all $\mathbb{Q}$-homology planes and for open smooth surfaces which are not of log general type.

13 pages. Comments are welcome!

References in corpus (3)

• Zero cycles with modulus and zero cycles on singular varieties
• 1-motivic sheaves and the Albanese functor
• On the interior motive of certain Shimura varieties: the case of Picard surfaces