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

TL;DR

This paper revisits a 1996 study on the relationship between the second Chow group and third unramified cohomology in smooth projective varieties, focusing on rationally connected varieties and their applications.

Contribution

It specializes a previous theoretical framework to rationally connected varieties, providing clearer insights and potential applications in algebraic geometry.

Findings

Clarifies the connection between Chow groups and unramified cohomology

Specializes results to rationally connected varieties

Provides applications in algebraic geometry

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.