English

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.

Keywords

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

R2 v1 2026-06-22T00:12:04.760Z