Grothendieck--Serre for constant reductive group schemes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913606388416512 |
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| author | Guo, Ning Liu, Fei |
| author_facet | Guo, Ning Liu, Fei |
| contents | The Grothendieck-Serre conjecture predicts that on a regular local ring, no nontrivial reductive torsor becomes trivial over the fraction field. While this conjecture has been proven in the equicharacteristic case, it remains open in the mixed characteristic case. This article establishes a generalized version of the conjecture over Prüfer bases for constant reductive group schemes. In particular, the Noetherian restriction of our main result settles the constant, unramified case of the Grothendieck-Serre conjecture. Along the way, inspired by the recent preprint of Cesnavicius, we also prove several versions of the Nisnevich conjecture in our context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_12460 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Grothendieck--Serre for constant reductive group schemes Guo, Ning Liu, Fei Algebraic Geometry Primary 14F22, Secondary 14F20, 14G22, 16K50 The Grothendieck-Serre conjecture predicts that on a regular local ring, no nontrivial reductive torsor becomes trivial over the fraction field. While this conjecture has been proven in the equicharacteristic case, it remains open in the mixed characteristic case. This article establishes a generalized version of the conjecture over Prüfer bases for constant reductive group schemes. In particular, the Noetherian restriction of our main result settles the constant, unramified case of the Grothendieck-Serre conjecture. Along the way, inspired by the recent preprint of Cesnavicius, we also prove several versions of the Nisnevich conjecture in our context. |
| title | Grothendieck--Serre for constant reductive group schemes |
| topic | Algebraic Geometry Primary 14F22, Secondary 14F20, 14G22, 16K50 |
| url | https://arxiv.org/abs/2301.12460 |