连通代数群的逆伽罗瓦问题

Pub Date : 2024-06-27 DOI:10.1007/s00031-024-09865-0

Michel Brion, Stefan Schröer

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引用次数: 0

摘要

我们证明，任意基域上有限类型的每个连通群方案与某个投影几何积分方案的自变群方案内的同构分量同构。主要内容包括嵌入光滑群方案、等变完备性、轨道闭合的吹大、凯勒微分的拟合理想和布兰查德定理。

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The Inverse Galois Problem for Connected Algebraic Groups

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.

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