Generically isotropic reductive group schemes are locally isotropic

Published 10 Mar 2023 in math.AG | (2303.05853v2)

Abstract: Let $R$ be a semilocal geometrically factorial Noetherian domain of characteristic zero. We show that a reductive $R$-group scheme is isotropic if it is generically isotropic. We derive various consequences, in particular for the Grothenieck-Serre conjecture and for homotopic invariance of torsors.

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Roman Fedorov

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