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arXiv · 2303.05853

Generically isotropic reductive group schemes are locally isotropic

Roman Fedorov
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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. 2023-03-10. Generically isotropic reductive group schemes are locally isotropic. https://arxiv.org/abs/2303.05853

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