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Article Dans Une Revue Inventiones Mathematicae Année : 2007

Unramified cohomology of degree 3 and Noether’s problem

Emmanuel Peyre

Résumé

Let $G$ be a finite group and $W$ be a faithful representation of $G$ over {\bf C}. The group $G$ acts on the field of rational functions $\mathbf C(W)$. The aim of this paper is to give a description of the unramified cohomology group of degree 3 of the field of invariant functions $\mathbf C(W)^G$ in terms of the cohomology of $G$ when $G$ is a group of odd order. This enables us to give an example of a group for which this field is not rational, although its unramified Brauer group is trivial.

Dates et versions

hal-00131640 , version 1 (17-02-2007)

Identifiants

Citer

Emmanuel Peyre. Unramified cohomology of degree 3 and Noether’s problem. Inventiones Mathematicae, 2007, 171 (1), pp.191 - 225. ⟨10.1007/s00222-007-0080-z⟩. ⟨hal-00131640⟩

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