English

Descente galoisienne sur le second groupe de Chow : mise au point et applications

Algebraic Geometry 2015-06-02 v5 K-Theory and Homology

Abstract

Connections between the second Chow group of a smooth projective variety and its third unramified cohomology group, with coefficients the roots of unity twisted twice, feature in several recent works. In this note we revisit a 1996 paper by B. Kahn and specialize it to various types of rationally connected varieties.

Keywords

Cite

@article{arxiv.1302.3215,
  title  = {Descente galoisienne sur le second groupe de Chow : mise au point et applications},
  author = {Jean-Louis Colliot-Thélène},
  journal= {arXiv preprint arXiv:1302.3215},
  year   = {2015}
}

Comments

In French. Final version, to appear in Documenta math. Section 5 contains a discussion of the universal unramified third cohomology group for Fano hypersurfaces, and in particular for cubic hypersurfaces