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Sbornik: Mathematics, 2020, Volume 211, Issue 3, Pages 466–480
DOI: https://doi.org/10.1070/SM9304 (Mi sm9304) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Birational automorphisms of Severi-Brauer surfaces

С. A. Shramovab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b National Research University Higher School of Economics, Moscow, Russia
English version PDF (493 kB) Citations (5) Russian version article
References:
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DOI: https://doi.org/10.1070/SM9304
Abstract: We prove that a finite group acting by birational automorphisms of a nontrivial Severi-Brauer surface over a field of characteristic zero contains a normal abelian subgroup of index at most 3. Also, we find an explicit bound for the orders of such finite groups in the case when the base field contains all roots of 1.
Bibliography: 25 titles.
Keywords: Severi-Brauer surface, group of birational automorphisms.
Funding agency Grant number
HSE Basic Research Program
Ministry of Education and Science of the Russian Federation 5-100
Contest «Young Russian Mathematics»
Foundation for the Advancement of Theoretical Physics and Mathematics BASIS
This research was carried out with the support of the HSE University Basic Research Program, Russian Academic Excellence Project “5-100”, the Young Russian Mathematics award, and the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”.
Received: 09.07.2019 and 29.11.2019
Bibliographic databases:
Document Type: Article
UDC: 512.76
MSC: 14E07, 14J99
Language: English
Original paper language: Russian
Citation: С. A. Shramov, “Birational automorphisms of Severi-Brauer surfaces”, Sb. Math., 211:3 (2020), 466–480
Citation in format AMSBIB
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\by С.~A.~Shramov
\paper Birational automorphisms of Severi-Brauer surfaces
\jour Sb. Math.
\yr 2020
\vol 211
\issue 3
\pages 466--480
\mathnet{http://mi.mathnet.ru/eng/sm9304}
\crossref{https://doi.org/10.1070/SM9304}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4070054}
\zmath{https://zbmath.org/?q=an:1445.14025}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2020SbMat.211..466S}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85087448833}
Linking options:
  • https://www.mathnet.ru/eng/sm9304
  • https://doi.org/10.1070/SM9304
  • https://www.mathnet.ru/eng/sm/v211/i3/p169
    • This publication is cited in the following 5 articles:
    1. A. Trepalin, “Birational classification of pointless del Pezzo surfaces of degree 8”, European Journal of Mathematics, 9:1 (2023), 2  crossref  mathscinet
    2. Shramov C., “Finite Groups Acting on Severi-Brauer Surfaces”, Eur. J. Math., 7:2 (2021), 591–612  crossref  mathscinet  isi  scopus
    3. A. S. Trepalin, “Quotients of Severi–Brauer Surfaces”, Dokl. Math., 104:3 (2021), 390  mathnet  crossref  crossref  zmath  elib
    4. С. A. Shramov, “Non-Abelian Groups Acting on Severi–Brauer Surfaces”, Math. Notes, 108:6 (2020), 916–917  mathnet  crossref  crossref  mathscinet  isi  elib
    5. C. Shramov, “Automorphisms of cubic surfaces without points”, Int. J. Math., 31:11 (2020), 2050083  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:517
    Russian version PDF:60
    English version PDF:43
    References:55
    First page:22
     
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