On a base change conjecture for higher zero-cycles

We show the surjectivity of a restriction map for higher $(0, 1)$-cycles for a smooth projective scheme over an excellent henselian discrete valuation ring. This gives evidence for a conjecture by Kerz, Esnault and Wittenberg saying that base change holds for such schemes in general for motivic cohomology in degrees $(i, d)$ for fixed $d$ being the relative dimension over the base. Furthermore, the restriction map we study is related to a finiteness conjecture for the $n$-torsion of $\mathrm{CH}_0 (X)$, where $X$ is a variety over a $p$-adic field.

Keywords

higher zero-cycles, restriction map, $n$-torsion

2010 Mathematics Subject Classification

14C25

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Received 12 February 2017

Received revised 17 May 2017

Published 20 December 2017