The inverse Galois problem for connected algebraic groups
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929399174004736 |
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| author | Brion, Michel Schröer, Stefan |
| author_facet | Brion, Michel Schröer, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_08117 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The inverse Galois problem for connected algebraic groups Brion, Michel Schröer, Stefan Algebraic Geometry 14L15, 14G17, 14J50 (Primary) 14M20, 17B50, 13N15 (Secondary) 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. |
| title | The inverse Galois problem for connected algebraic groups |
| topic | Algebraic Geometry 14L15, 14G17, 14J50 (Primary) 14M20, 17B50, 13N15 (Secondary) |
| url | https://arxiv.org/abs/2205.08117 |