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arXiv · 1111.1590

Orthogonal representations of affine group schemes and twists of symmetric bundles

Philippe Cassou-Noguès·Ted Chinburg·Baptiste Morin·Martin Taylor
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Abstract

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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Philippe Cassou-Noguès, Ted Chinburg, Baptiste Morin, Martin Taylor. 2011-11-07. Orthogonal representations of affine group schemes and twists of symmetric bundles. https://arxiv.org/abs/1111.1590

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