Vol. 3, No. 3, 2018

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

Qizheng Yin and Yi Zhu

Vol. 3 (2018), No. 3, 379–393

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 -homology planes and for open smooth surfaces which are not of log general type.

Bloch's conjecture, open algebraic surfaces, $\mathbb{Q}$-homology planes, Suslin homology, mixed motives
Mathematical Subject Classification 2010
Primary: 14C15, 14C25, 14F42
Received: 28 March 2016
Revised: 28 November 2017
Accepted: 14 December 2017
Published: 16 July 2018
Qizheng Yin
Beijing International Center for Mathematical Research
Peking University
Yi Zhu
Pure Mathematics
University of Waterloo
Waterloo, ON