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arXiv · 2107.01950

R-equivalence on group schemes

Philippe Gille·A Stavrova
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Abstract

We define R-equivalence for group schemes over a semilocal ring and relate this with rational properties. Two main cases are investigated: tori and isotropic semisimple simply connected group schemes where we show in certain cases that R-equivalence coincide with Karoubi-Villamayor equivalence and is also related to the Kneser-Tits problem in this setting. Finally we construct specialization maps for R-equivalence in the case of regular algebras containing a field.

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Philippe Gille, A Stavrova. 2021-07-05. R-equivalence on group schemes. https://arxiv.org/abs/2107.01950

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