Group schemes over LG-rings and applications to cancellation theorems and Azumaya algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929734963691520 |
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| author | Gille, Philippe Neher, Erhard |
| author_facet | Gille, Philippe Neher, Erhard |
| contents | We prove several results on reductive group schemes over LG-rings, e.g., existence of maximal tori and conjugacy of parabolic subgroups. These were proven in SGA3 for the special case of semilocal rings. We apply these results to establish cancellation theorems for hermitian and quadratic forms over LG-rings and show that the Brauer classes of Azumaya algebras over connected LG-rings have a unique representative and allow Brauer decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02021 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Group schemes over LG-rings and applications to cancellation theorems and Azumaya algebras Gille, Philippe Neher, Erhard Algebraic Geometry Rings and Algebras We prove several results on reductive group schemes over LG-rings, e.g., existence of maximal tori and conjugacy of parabolic subgroups. These were proven in SGA3 for the special case of semilocal rings. We apply these results to establish cancellation theorems for hermitian and quadratic forms over LG-rings and show that the Brauer classes of Azumaya algebras over connected LG-rings have a unique representative and allow Brauer decomposition. |
| title | Group schemes over LG-rings and applications to cancellation theorems and Azumaya algebras |
| topic | Algebraic Geometry Rings and Algebras |
| url | https://arxiv.org/abs/2407.02021 |