A classification of torsors over Laurent polynomial rings

Vladimir Chernousov (1) , Philippe Gille (2, 3) , Arturo Pianzola (1)

1 University of Alberta
2 IMAR - "Simion Stoilow" Institute of Mathematics
3 AGL - Algèbre, géométrie, logique

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.

Mots clés: Reductive group scheme; multiloop algebra.; torsor

Domaines: Anneaux et algèbres [math.RA]

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