Orthogonal representations of affine group schemes and twists of symmetric bundles

Philippe Cassou-Noguès (1) , Ted Chinburg (2) , Baptiste Morin (3) , Martin Taylor (4)

1 IMB - Institut de Mathématiques de Bordeaux
2 Department of Mathematics [Philadelphia]
3 UT3 - Université Toulouse III - Paul Sabatier
4 MI - Mathematical Institute [Oxford]

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.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Philippe Cassou-Noguès, Ted Chinburg, Baptiste Morin, Martin Taylor. Orthogonal representations of affine group schemes and twists of symmetric bundles. 2011. ⟨hal-01027779⟩