On the cycle class map for zero-cycles over local fields
Algebraic Geometry
2019-11-21 v4 Number Theory
Abstract
We study the Chow group of zero-cycles of smooth projective varieties over local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus, over local fields of residue characteristic different from l. The same statement holds for semistable K3 surfaces defined over C((t)), but does not hold in general for surfaces over strictly local fields.
Cite
@article{arxiv.1305.1182,
title = {On the cycle class map for zero-cycles over local fields},
author = {Hélène Esnault and Olivier Wittenberg},
journal= {arXiv preprint arXiv:1305.1182},
year = {2019}
}
Comments
37 pages (with an appendix by Spencer Bloch); bibliography updated, final version