5 papers
Loop torsors. Theory and applications
Philippe Gille, Vladimir Chernousov, Arturo Pianzola
Loop torsors over Laurent polynomial rings in characteristic 0 were originally introduced in relation to infinite dimensional Lie theory. Applications to other areas require a theo…
Loop torsors and Abhyankar's lemma
Philippe Gille
We define the notion of loop torsors under certain group schemes defined over the localization of a regular henselian ring A at a strict normal crossing divisor D. We provide a Gal…
Fiberwise criteria for Twisted Forms of Algebraic Structures
Philippe Gille, Arturo Pianzola
We provide a criterion for certain algebraic objects over Jacobson schemes to be forms of each other based on their behaviour at closed fibres. This criterion permits to answer a q…
A classification of torsors over Laurent polynomial rings
Vladimir Chernousov, Philippe Gille, Arturo Pianzola
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 , we show th…
Reduction of structure for torsors over semilocal rings
V. Chernousov, Ph. Gille, Z. Reichstein
Let G be a reductive affine group scheme defined over a semilocal ring k. Assume that either G is semisimple or k is normal and noetherian. We show that G has a finite k-subgroup S…