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arXiv · 1510.05621

A classification of torsors over Laurent polynomial rings

Vladimir Chernousov·Philippe Gille·Arturo Pianzola
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Abstract

Let R\_n be the ring of Laurent polynomials in n variables over a field k of characteristic zero and let K\_n be its fraction field.Given a linear algebraic k-group $G$, we show that a K\_n-torsor under G which is unramified with respect to X=Spec(R\_n)extends to a unique toral R\_n-torsor under G. This result, in turn, allows us to classify all G-torsors over R\_n.

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Vladimir Chernousov, Philippe Gille, Arturo Pianzola. 2015-10-19. A classification of torsors over Laurent polynomial rings. https://arxiv.org/abs/1510.05621

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