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 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.
Citation
P. Cassou-Noguès. T. Chinburg. B. Morin. M. J. Taylor. "Hopf algebras and quadratic forms." Illinois J. Math. 58 (2) 413 - 442, Summer 2014. https://doi.org/10.1215/ijm/1436275492
Information