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Abstract: 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 thatG has a finite k-subgroup S such that the natural map H^1R, S -> H^1R, Gis surjective for every semilocal ring R containing k. In other words,G-torsors over SpecR admit reduction of structure to S. We also show that thenatural map H^1X, S -> H^1X, G is surjective in several other contexts,under suitable assumptions on the base ring k, the scheme X-k and the groupscheme G-k. These results have already been used to study loop algebras as wellas essential dimension of connected algebraic groups in prime characteristic.Additional applications are presented at the end of this paper.



Autor: V. Chernousov, Ph. Gille, Z. Reichstein

Fuente: https://arxiv.org/







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