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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 501, Pages 84–88
DOI: https://doi.org/10.31857/S2686954321060175 (Mi danma17) 		 
MATHEMATICS

Quotients of Severi–Brauer surfaces

A. S. Trepalinab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Laboratory of algebraic geometry and its applications, National Research University "Higher School of Economics" (HSE), Moscow
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DOI: https://doi.org/10.31857/S2686954321060175
Abstract: We show that a quotient of a non-trivial Severi–Brauer surface $S$ over arbitrary field $\mathbb k$ of characteristic 0 by a finite group $G\subset\operatorname{Aut}(S)$ is $\mathbb k$-rational if and only if $|G|$ is divisible by 3. Otherwise, the quotient is birationally equivalent to $S$.
Keywords: Severi–Brauer surfaces, rationality problems, Brauer group, minimal model program.
Funding agency Grant number
HSE Academic Fund Programme
The study has been funded within the framework of the HSE University Basic Research Program.
Presented: A. N. Parshin
Received: 05.08.2021
Revised: 26.10.2021
Accepted: 27.10.2021
Bibliographic databases:
Document Type: Article
UDC: 512.774.4
Language: Russian
Citation: A. S. Trepalin, “Quotients of Severi–Brauer surfaces”, Dokl. RAN. Math. Inf. Proc. Upr., 501 (2021), 84–88
Citation in format AMSBIB
\Bibitem{Tre21}
\by A.~S.~Trepalin
\paper Quotients of Severi--Brauer surfaces
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2021
\vol 501
\pages 84--88
\mathnet{http://mi.mathnet.ru/danma17}
\crossref{https://doi.org/10.31857/S2686954321060175}
\zmath{https://zbmath.org/?q=an:7503285}
\elib{https://elibrary.ru/item.asp?id=47371424}
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