2002/12/03 by Emmanuel Peyre
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Cohomology #Degree (music) #Equivariant cohomology #Group (periodic table) #Group cohomology #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Mathematical physics #Mathematics #Noether's theorem #Pure mathematics #math.AG #math.KT #msc:12G05 #msc:14E08 #msc:14F43 #Étale cohomology
paper · pdf · doi:10.1007/s00222-007-0080-z
published as Invent. Math. 171, No 1, 191-225 (2008)
arxiv created 2002/12/03 · openalex publication_date 2007/09/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.