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.

中文翻译：

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维特集团行动的轨道封闭

我们证明了对任何素p存在二维维特组的代数动作w ^ ₂（p）上的代数簇X，使得闭合在X的w ^ ₂（p一些点的）-orbit的x∈X包含无限多个W ₂（p）轨道。这涉及到以下问题：从特征零的情况到特征p的情况，扩展了连通仿射代数群G的分类，使得每个代数G-都具有稠密开放G轨道仅包含有限的多个G轨道。