Illinois Journal of Mathematics

Hopf algebras and quadratic forms

P. Cassou-Noguès, T. Chinburg, B. Morin, and M. J. Taylor

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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.

Article information

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11E81: Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24] 16W30


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.

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