Generically isotropic reductive group schemes are locally isotropic

Fedorov, Roman

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Generically isotropic reductive group schemes are locally isotropic

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Fedorov, Roman
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2303.05853
(Preprint)

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2303.05853.pdf
(Preprint), 253KB

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Citation

Fedorov, R. (submitted). Generically isotropic reductive group schemes are locally isotropic.

Cite as: https://hdl.handle.net/21.11116/0000-000F-9BD7-0

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.