The inverse Galois problem for connected algebraic groups

Publication date: 17 May 2022

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 K"ahler differentials, and Blanchard's Lemma.

Mathematics Subject Classification ID

Rational and unirational varieties (14M20) Derivations and commutative rings (13N15) Modular Lie (super)algebras (17B50) Automorphisms of surfaces and higher-dimensional varieties (14J50) Group schemes (14L15) Positive characteristic ground fields in algebraic geometry (14G17)

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