A Proof of the Barsotti-Chevalley Theorem on Algebraic Groups
Algebraic Geometry
2013-12-10 v2 Group Theory
Abstract
A fundamental theorem of Barsotti and Chevalley states that every smooth algebraic group over a perfect field is an extension of an abelian variety by a smooth affine algebraic group. In 1956 Rosenlicht gave a short proof of the theorem. In this expository article, we explain his proof in the language of modern algebraic geometry.
Cite
@article{arxiv.1311.6060,
title = {A Proof of the Barsotti-Chevalley Theorem on Algebraic Groups},
author = {James S. Milne},
journal= {arXiv preprint arXiv:1311.6060},
year = {2013}
}
Comments
v2 Expanded exposition; fixed gap