Trudy Matematicheskogo Instituta imeni V.A. Steklova
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy Mat. Inst. Steklova: Year: Volume: Issue: Page: Find

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

Orbit Closures of the Witt Group Actions

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

Full text: PDF file (160 kB)
First page: PDF file
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 512.743
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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000520962900011} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85083234297} 

• http://mi.mathnet.ru/eng/tm4024
• https://doi.org/10.4213/tm4024
• http://mi.mathnet.ru/eng/tm/v307/p212

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Popov V.L., “Algebraic Groups Whose Orbit Closures Contain Only Finitely Many Orbits”, Transform. Groups
•  Number of views: This page: 381 References: 8 First page: 3