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 greater than or 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.
On the essential dimension of infinitesimal group schemes
VISTOLI, ANGELO
2013
Abstract
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 greater than or 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.File in questo prodotto:
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