Finite subgroups of automorphism groups of Severi--Brauer varieties of prime degree
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910178220179456 |
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| author | Sonina, Alexandra |
| author_facet | Sonina, Alexandra |
| contents | We classify finite subgroups of automorphism groups of non-trivial Severi--Brauer varieties of dimension $q-1$, where $q \geqslant 3$ is a prime number, over an arbitrary field. We also construct families of examples, namely, for every consistent set of finite groups, we construct a field together with a non-trivial Severi--Brauer variety over that field such that every group in the set acts on the constructed variety. Additionally, we show that non-trivial Severi--Brauer varieties of dimension $q-1$, where $q \geqslant 3$ is a prime number, over a field of characteristic not equal to $q$ are not $G$-birationally rigid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03916 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite subgroups of automorphism groups of Severi--Brauer varieties of prime degree Sonina, Alexandra Algebraic Geometry We classify finite subgroups of automorphism groups of non-trivial Severi--Brauer varieties of dimension $q-1$, where $q \geqslant 3$ is a prime number, over an arbitrary field. We also construct families of examples, namely, for every consistent set of finite groups, we construct a field together with a non-trivial Severi--Brauer variety over that field such that every group in the set acts on the constructed variety. Additionally, we show that non-trivial Severi--Brauer varieties of dimension $q-1$, where $q \geqslant 3$ is a prime number, over a field of characteristic not equal to $q$ are not $G$-birationally rigid. |
| title | Finite subgroups of automorphism groups of Severi--Brauer varieties of prime degree |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2508.03916 |