连通代数群的逆伽罗瓦问题

IF 0.4 3区数学 Q4 MATHEMATICS

Transformation Groups 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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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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来源期刊

Transformation Groups 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

100

审稿时长

9 months

期刊介绍： Transformation Groups will only accept research articles containing new results, complete Proofs, and an abstract. Topics include: Lie groups and Lie algebras; Lie transformation groups and holomorphic transformation groups; Algebraic groups; Invariant theory; Geometry and topology of homogeneous spaces; Discrete subgroups of Lie groups; Quantum groups and enveloping algebras; Group aspects of conformal field theory; Kac-Moody groups and algebras; Lie supergroups and superalgebras.