The inverse Galois problem for connected algebraic groups
Algebraic Geometry
2024-06-26 v2
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.
Keywords
Cite
@article{arxiv.2205.08117,
title = {The inverse Galois problem for connected algebraic groups},
author = {Michel Brion and Stefan Schröer},
journal= {arXiv preprint arXiv:2205.08117},
year = {2024}
}
Comments
Minor changes. Final version, to appear in Transformation Groups