A Proof of the Barsotti-Chevalley Theorem on Algebraic Groups

2013/11/23 by J. S. Milne, Milne, James S.
Mathematics · #14L15 20G07 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1311.6060

openalex publication_date 2013/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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