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PreprintarXiv licencearXiv

Finite Subgroups of Birational Automorphism Groups of Severi--Brauer Surfaces

  • Alexandra Sonina
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Abstract

We prove that a finite group acting birationally on a non-trivial Severi--Brauer surface S over a field 𝕂 of positive characteristic not equal to $3$ is isomorphic either to a subgroup of group of biregular automorphisms of S𝕂per or to a subgroup of ΞΌ33, where ΞΌ3 is a cyclic group of order $3$ and 𝕂per is the perfect closure of a field 𝕂. Combined with results about classification of finite subgroups of the group of biregular automorphisms of S, this gives a classification of finite subgroups of the group of birational automorphisms of S.

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Cite

BibTeXRIS
BibTeX
@misc{sonina2026finite,
  title = {{Finite Subgroups of Birational Automorphism Groups of Severi--Brauer Surfaces}},
  author = {Alexandra Sonina},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.09981},
  eprint = {2611.09981},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.09981},
}
RIS
TY  - UNPB
TI  - Finite Subgroups of Birational Automorphism Groups of Severi--Brauer Surfaces
AU  - Alexandra Sonina
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.09981
UR  - https://arxiv.org/abs/2611.09981
AB  - We prove that a finite group acting birationally on a non-trivial Severi--Brauer surface S over a field 𝕂 of positive characteristic not equal to $3$ is isomorphic either to a subgroup of group of biregular automorphisms of S_𝕂^per or to a subgroup of ΞΌ^3_3, where ΞΌ_3 is a cyclic group of order $3$ and 𝕂^per is the perfect closure of a field 𝕂. Combined with results about classification of finite subgroups of the group of biregular automorphisms of S, this gives a classification of finite subgroups of the group of birational automorphisms of S.
ER  -