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On the essential dimension of infinitesimal group schemes

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.

preprint2010arXivOpen access
Dajano TossiciAngelo Vistoli
math.AGmath.NT
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Dajano TossiciAngelo Vistoli

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