Homology, Homotopy and Applications

Volume 20 (2018)

Number 1

On a base change conjecture for higher zero-cycles

Pages: 59 – 68

DOI: https://dx.doi.org/10.4310/HHA.2018.v20.n1.a4


Morten Lüders (Department of Mathematics, University of Regensburg, Germany)


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.


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

2010 Mathematics Subject Classification


Received 12 February 2017

Received revised 17 May 2017

Published 20 December 2017