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A classification of torsors over Laurent polynomial rings

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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Contributor : Philippe Gille Connect in order to contact the contributor
Submitted on : Monday, October 19, 2015 - 3:31:33 PM
Last modification on : Monday, June 28, 2021 - 2:26:06 PM
Long-term archiving on: : Thursday, April 27, 2017 - 6:50:15 AM


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  • HAL Id : hal-01217408, version 1
  • ARXIV : 1510.05621


Vladimir Chernousov, Philippe Gille, Arturo Pianzola. A classification of torsors over Laurent polynomial rings. Commentarii Mathematici Helvetici, European Mathematical Society, 2017, 92, pp.37-55. ⟨hal-01217408⟩



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