The inverse Galois problem for connected algebraic groups

2022/05/17 by Michel Brion, Stefan Schröer, Brion, Michel +1
Mathematics · #13N15 (Secondary) #14G17 #14J50 (Primary) 14M20 #14L15 #17B50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2205.08117

openalex publication_date 2022/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that each connected group scheme of finite type over an arbitrary ground field is isomorphic to the component of the identity inside the automorphism group scheme of some projective, geometrically integral scheme. The main ingredients are embeddings into smooth group schemes, equivariant completions, blow-ups of orbit closures, Fitting ideals for Kähler differentials, and Blanchard's Lemma.

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