Vol. 5, No. 6, 2011

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ISSN: 1944-7833 (e-only)
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Sur le groupe de Chow de codimension deux des variétés sur les corps finis

Alena Pirutka

Vol. 5 (2011), No. 6, 803–817
Abstract

En utilisant la construction de Colliot-Thélène et Ojanguren, on donne un exemple d’une variété projective et lisse géométriquement rationnelle X, définie sur un corps fini Fp, telle que d’une part le groupe Hnr3(X, 2) est non nul et, d’autre part, l’application CH2(X) CH2(X ×FpF ̄p)Gal(F ̄pFp) n’est pas surjective.

Using a construction of Colliot-Thélène and Ojanguren, we exhibit an example of a smooth projective geometrically rational variety X defined over a finite field Fp, such that the group Hnr3(X, 2) is nonzero and the map CH2(X) CH2(X ×FpF ̄p)Gal(F ̄pFp) is not surjective.

Keywords
groupes de Chow, cohomologie non ramifiée, Chow groups, unramified cohomology
Mathematical Subject Classification 2000
Primary: 14C25
Milestones
Received: 14 May 2010
Revised: 12 October 2010
Accepted: 15 November 2010
Published: 2 April 2012
Authors
Alena Pirutka
École Normale Supérieure
45 rue d’Ulm
75230 Paris
France