Orthogonal representations of affine group schemes and twists of symmetric bundles

Details Orthogonal representations of affine group schemes and twists of symmetric bundles Orthogonal representations of affine group schemes and twists of symmetric bundles

2011-11-07

arxiv.org/abs/1111.1590v1

Mathematics

Algebraic Geometry

31 p

Scientific paper

Following Serre's initial work, a number of authors have considered twists of quadratic forms on a scheme Y by torsors of a finite group G, together with formulas for the Hasse-Witt invariants of the twisted form. In this paper we take the base scheme Y to be affine and consider non-constant groups schemes G. There is a fundamental new feature in this case - in that the torsor may now be ramified over Y. The natural framework for handling the case of a non-constant group scheme over the affine base is provided by the quadratic theory of Hopf-algebras.

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