Infinitesimal rational actions on curves

Abstract: For any finite $k$-group scheme $G$ acting rationally on a $k$-variety $X$, if the action is generically free then the dimension of $Lie (G)$ is upper bounded by the dimension of the variety. This inequality turns out to be also a sufficient condition for the existence of such actions, when $k$ is a perfect field of positive characteristic and $G$ is infinitesimal commutative trigonalizable. In this talk, we will specialize to the case in which $X$ is a curve. First, we will give an explicit description of all the infinitesimal commutative unipotent group schemes $G$ with a generically free rational action on $X$ when $k$ is algebraically closed. We will then see how these actions can be constructed, focusing on the case in which $G$ is the $p$-torsion of a supersingular elliptic curve.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html