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Hélène Esnault, Olivier Wittenberg
On the cycle class map for zero-cyclesocal fields
Annales scientifiques de l'ENS 49, fascicule 2 (2016), 483-520

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Résumé :
Sur l'application classe de cycle pour les zéro-cycles sur les corps locaux
Nous étudions le groupe de Chow des -cycles des variétés projectives et lisses sur les corps locaux et strictement locaux. Nous prouvons en particulier l'injectivité de l'application classe de cycle vers la cohomologie -adique entière pour de nombreuses surfaces de genre géométrique non nul, sur les corps locaux de caractéristique résiduelle . Le même énoncé vaut pour les surfaces semi-stables définies sur ((t)) , mais ne vaut pas en général pour les surfaces sur les corps strictement locaux.

Mots-clefs : Zéro-cycles, corps locaux, surfaces K3.

Abstract:
We study the Chow group of -cycles of smooth projective varieties over local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral -adic cohomology for a large class of surfaces with positive geometric genus, over local fields of residue characteristic . The same statement holds for semistable surfaces defined over ((t)) , but does not hold in general for surfaces over strictly local fields.

Keywords: Zero-cycles, local fields, K3 surfaces.

Class. math. : 14C15; 14G20, 14J28, 14D06

ISSN : 0012-9593
Publié avec le concours de : Centre National de la Recherche Scientifique

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