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arXiv · 2312.01765

Infinitesimal rational actions

Bianca Gouthier
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Abstract

For any finite $k$-group scheme $G$ acting rationally on a $k$-variety, if the action is generically free then the dimension of $\mathrm{Lie} (G)$ is upper bounded by the dimension of the variety. We show that this is the only obstruction when $k$ is a perfect field of positive characteristic and $G$ is infinitesimal commutative trigonalizable. We also give necessary conditions to have faithful rational actions of infinitesimal commutative trigonalizable group schemes on varieties, and (different) sufficient conditions in the unipotent case over a perfect field.

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Bianca Gouthier. 2023-12-04. Infinitesimal rational actions. https://doi.org/10.1090/tran/9413

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