Realisation of linear algebraic groups as automorphism groups

Mathieu Florence

Realisation of linear algebraic groups as automorphism groups

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arxiv 2311.04118 v3 pith:SIEYVTJX submitted 2023-11-07 math.AG

Mathieu Florence This is my paper · ORCID

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keywords algebraicautomorphismgroupgroupslinearprojectivesmoothalong

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abstract

Let $G$ be a linear algebraic group, over a field $F$. We show that $G$ is isomorphic to the automorphism group scheme of a smooth projective $F$-variety, defined as the blow-up of a projective space, along a suitable smooth subvariety.

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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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