Unramified cohomology of degree 3 and Noether's problem

Details Unramified cohomology of degree 3 and Noether's problem Unramified cohomology of degree 3 and Noether's problem

2002-12-03

arxiv.org/abs/math/0212039v1

Invent. Math. 171, No 1, 191-225 (2008)

Mathematics

Algebraic Geometry

Scientific paper

10.1007/s00222-007-0080-z

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.

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