On the essential dimension of infinitesimal group schemes
Algebraic Geometry
2010-10-26 v3 Number Theory
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 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.
Keywords
Cite
@article{arxiv.1001.3988,
title = {On the essential dimension of infinitesimal group schemes},
author = {Dajano Tossici and Angelo Vistoli},
journal= {arXiv preprint arXiv:1001.3988},
year = {2010}
}
Comments
11 pages; proof of Theorem 1.2 slightly changed; improved the exposition in section 4 and added Proposition 4.3. Accepted for publication in The American Journal of Mathematics