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On the essential dimension of infinitesimal group schemes
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 135, Number 1, February 2013
- pp. 103-114
- 10.1353/ajm.2013.0007
- Article
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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.