2004/04/11 by Ph. Cassou-Nogues, Ph. Cassou-Noguès, Boas Erez +5
Mathematics · #11E70 #14E20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.AG #math.NT #msc:11E70 #msc:14E20
paper · pdf · doi:10.48550/arxiv.math/0404219
58 pages
arxiv created 2004/04/11 · openalex publication_date 2004/04/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish comparison results between the Hasse-Witt invariants wt(E) of a symmetric bundle E over a scheme and the invariants of one of its twists Eα. For general twists we describe the difference between wt(E) and wt(Eα) up to terms of degree 3. Next we consider a special kind of twist, which has been studied by A. Fröhlich. This arises from twisting by a cocycle obtained from an orthogonal representation. We show how to explicitly describe the twist for representations arising from very general tame actions. This involves the ``square root of the inverse different'' which Serre, Esnault, Kahn, Viehweg and ourselves had studied before. For torsors we show that, in our geometric set-up, Jardine's generalization of Frohlich's formula holds. The case of genuinely tamely ramified actions is geometrically more involved and leads us to introduce a ramification invariant which generalises in higher dimension the invariant introduced by Serre for curves.