English

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.

Keywords

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