Algebra & Number Theory

Sur le groupe de Chow de codimension deux des variétés sur les corps finis

Alena Pirutka

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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.

Article information

Source
Algebra Number Theory, Volume 5, Number 6 (2011), 803-817.

Dates
Received: 14 May 2010
Revised: 12 October 2010
Accepted: 15 November 2010
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513729691

Digital Object Identifier
doi:10.2140/ant.2011.5.803

Mathematical Reviews number (MathSciNet)
MR2923728

Zentralblatt MATH identifier
1245.14025

Subjects
Primary: 14C25: Algebraic cycles

Keywords
groupes de Chow cohomologie non ramifiée Chow groups unramified cohomology

Citation

Pirutka, Alena. Sur le groupe de Chow de codimension deux des variétés sur les corps finis. Algebra Number Theory 5 (2011), no. 6, 803--817. doi:10.2140/ant.2011.5.803. https://projecteuclid.org/euclid.ant/1513729691


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