The isotropic loop reductive torsor conjecture

Let G\mathfrak G be a loop reductive group scheme over RnR_n, and suppose that all semisimple quotients of G\mathfrak G are isotropic. Isotropic loop reductive torsor conjecture. Then

HZar1(Rn,G)=1.H^1_{Zar}(R_n,\mathfrak G)=1.

This would generalize the preceding example for reductive groups whose semisimple quotients are isotropic, where rationally trivial torsors are trivial. The source presents this as an expected generalization and gives no resolution.

Sources & referencesView supporting material

Primary source

Vladimir Chernousov, Philippe Gille and Arturo Pianzola, “A classification of torsors over Laurent polynomial rings”, arXiv:1510.05621 (2015).

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