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

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