
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 twodimensional 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
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http://mi.mathnet.ru/eng/tm4024
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