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arxiv: 1311.6060 · v2 · submitted 2013-11-23 · 🧮 math.AG · math.GR

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A Proof of the Barsotti-Chevalley Theorem on Algebraic Groups

James S. Milne
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classification 🧮 math.AG math.GR
keywords algebraicprooftheoremgroupsmoothabelianaffinearticle
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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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  1. Theorems of Bertini and Chevalley

    math.AG 2026-05 unverdicted novelty 4.0

    A short proof is given for Chevalley's theorem on algebraic groups as extensions of Abelian varieties by linear groups, while addressing Bertini's irreducibility theorem.