Dajano Tossici and Angelo Vistoli: On the essential dimension of infinitesimal group schemes

dajano.tossici@sns.it, angelo.vistoli@sns.it

Submission: 2010, Jan 22

We discuss essential dimension of group schemes, with particular attention to infinitesimal group schemes. We prove that the essential dimension of a group scheme of finite type over a field k is at least equal to the difference between the dimension of its Lie algebra and its dimension. Furthermore, we show that the essential dimension of a trigonalizable group scheme of length p^{n} over a field of characteristic p>0 is at most n. We give several examples.

2000 Mathematics Subject Classification: 14L20; 14L30

Keywords and Phrases: essential dimension, torsors, group schemes

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