R-equivalence on group schemes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909901153894400 |
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| author | Gille, Philippe Stavrova, A |
| author_facet | Gille, Philippe Stavrova, A |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_01950 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | R-equivalence on group schemes Gille, Philippe Stavrova, A Algebraic Geometry Rings and Algebras 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. |
| title | R-equivalence on group schemes |
| topic | Algebraic Geometry Rings and Algebras |
| url | https://arxiv.org/abs/2107.01950 |