Hom schemes for algebraic groups

2023/09/28 by Sean Cotner, Cotner, Sean
Mathematics · #14L40 #20G15 #20G35 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2309.16458

openalex publication_date 2023/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In SGA3, Demazure and Grothendieck showed that if G and H are smooth affine group schemes over a scheme S and G is reductive, then the functor of S-homomorphism G → H is representable. In this paper we extend this result to cover cases in which G is not reductive, with much simpler proofs. Our results apply in particular to parabolics over any base, and they are essentially optimal over a field. We also relate the closed orbits in Hom schemes to Serre's theory of complete reducibility, answer a question of Furter--Kraft, and provide many examples.

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