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 Tr. Mat. Inst. Steklova, Forthcoming paper (Mi tm4024)

Orbit closures of the Witt group actions

V. L. Popov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We prove that, for any prime integer $p\geqslant 2$, there exist an algebraic action of the two-dimensional Witt group $W_2(p)$ on an algebraic variety $X$ and a point $x\in X$ such that the closure of the $W_2(p)$-orbit of $x$ in $X$ contains infinitely many $W_2(p)$-orbits. This is related to the problem of extending from characteristic zero to characteristic $p$ the classification of connected affine algebraic groups $G$ such that there are only finitely many $G$-orbits in every algebraic $G$-variety containing a dense open $G$-orbit.

Document Type: Article
UDC: 512.743