Geodesic
Orbit Closures of the Witt Group Actions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 212-216.

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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. 
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     author = {Vladimir L. Popov},
     title = {Orbit {Closures} of the {Witt} {Group} {Actions}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/TM_2019_307_a10/}
}
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Vladimir L. Popov. Orbit Closures of the Witt Group Actions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 212-216. http://geodesic.mathdoc.fr/item/TM_2019_307_a10/

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