A Proof of the Barsotti-Chevalley Theorem on Algebraic Groups

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.

v2 Expanded exposition; fixed gap

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