Orbit Closures of the Witt Group Actions

Abstract

We prove that for any prime p there exists an algebraic action of the two-dimensional Witt group W2 (p) on an algebraic variety X such that the closure in X of the W2(p)-orbit of some point x ∈ X contains infinitely many W2(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.