On the cycle class map for zero-cycles over local fields (with an appendix by Spencer Bloch)

Hélène Esnault (1) , Olivier Wittenberg (2, 3)

1 Department of Mathematics and Computer Science
2 CNRS - Centre National de la Recherche Scientifique
3 DMA - Département de Mathématiques et Applications - ENS Paris

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.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Hélène Esnault, Olivier Wittenberg. On the cycle class map for zero-cycles over local fields (with an appendix by Spencer Bloch). Annales Scientifiques de l'École Normale Supérieure, 2016, 49 (2), pp.483-520. ⟨10.24033/asens.2288⟩. ⟨hal-02371560⟩