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The inverse Galois problem for connected algebraic groups

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arxiv 2205.08117 v2 pith:7HFK2QO5 submitted 2022-05-17 math.AG

Michel Brion , Stefan Schröer This is my paper · ORCID
classification math.AG
keywords groupschemeconnectedahleralgebraicarbitraryautomorphismblanchard
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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 K\"ahler differentials, and Blanchard's Lemma.

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  1. Generically trivial torsors under constant groups

    math.AG 2025-05 conditional novelty 8.0 of 10

    Every generically trivial torsor under a smooth group scheme over a smooth variety over any field is Zariski semilocally trivial, settling the Grothendieck-Serre question.

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