Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 58, Number 2 (2014), 413-442.
Hopf algebras and quadratic forms
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 group schemes $G$. Our main result describes these twists by a simple and explicit formula. 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.
Illinois J. Math., Volume 58, Number 2 (2014), 413-442.
Received: 17 October 2013
Revised: 29 January 2015
First available in Project Euclid: 7 July 2015
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Cassou-Noguès, P.; Chinburg, T.; Morin, B.; Taylor, M. J. Hopf algebras and quadratic forms. Illinois J. Math. 58 (2014), no. 2, 413--442. doi:10.1215/ijm/1436275492. https://projecteuclid.org/euclid.ijm/1436275492