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Trudy Mat. Inst. Steklova, 2019, Volume 307, Pages 212–216 (Mi tm4024)  

This article is cited in 1 scientific paper (total in 1 paper)

Orbit Closures of the Witt Group Actions

Vladimir L. Popov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: We prove that for any prime $p$ there exists an algebraic action of the two-dimensional Witt group $W_2(p)$ on an algebraic variety $X$ such that the closure in $X$ of the $W_2(p)$-orbit of some point $x\in X$ contains infinitely many $W_2(p)$-orbits. This is related to the problem of extending, from the case of characteristic zero to the case of characteristic $p$, the classification of connected affine algebraic groups $G$ such that every algebraic $G$-variety with a dense open $G$-orbit contains only finitely many $G$-orbits.

DOI: https://doi.org/10.4213/tm4024

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English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 307, 193–197

Bibliographic databases:

UDC: 512.743
Received: February 2, 2019
Revised: April 28, 2019
Accepted: April 30, 2019

Citation: Vladimir L. Popov, “Orbit Closures of the Witt Group Actions”, Algebra, number theory, and algebraic geometry, Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich, Trudy Mat. Inst. Steklova, 307, Steklov Mathematical Institute of RAS, Moscow, 2019, 212–216; Proc. Steklov Inst. Math., 307 (2019), 193–197

Citation in format AMSBIB
\Bibitem{Pop19}
\by Vladimir~L.~Popov
\paper Orbit Closures of the Witt Group Actions
\inbook Algebra, number theory, and algebraic geometry
\bookinfo Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich
\serial Trudy Mat. Inst. Steklova
\yr 2019
\vol 307
\pages 212--216
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4024}
\crossref{https://doi.org/10.4213/tm4024}
\elib{https://elibrary.ru/item.asp?id=43261050}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2019
\vol 307
\pages 193--197
\crossref{https://doi.org/10.1134/S0081543819060117}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Popov V.L., “Algebraic Groups Whose Orbit Closures Contain Only Finitely Many Orbits”, Transform. Groups  crossref  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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