微分方案的伽罗瓦理论

arXiv - MATH - Commutative Algebra Pub Date : 2024-07-30 DOI:arxiv-2407.21147

Ivan Tomašić, Behrang Noohi

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引用次数: 0

摘要

自 1883 年以来，Picard-Vessiot 理论一直被发展为与线性微分方程相关的微分域扩展的伽罗瓦理论。受 Janelidze 的分类伽罗瓦理论的启发，并通过使用适用于代数几何情况的前分类下降的新方法，我们发展了一种适用于微分方案形态的伽罗瓦理论，并极大地概括了线性 Picard-Vessiot 理论以及 Kolchin 的强正则理论。

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Galois theory of differential schemes

Since 1883, Picard-Vessiot theory had been developed as the Galois theory of differential field extensions associated to linear differential equations. Inspired by categorical Galois theory of Janelidze, and by using novel methods of precategorical descent applied to algebraic-geometric situations, we develop a Galois theory that applies to morphisms of differential schemes, and vastly generalises the linear Picard-Vessiot theory, as well as the strongly normal theory of Kolchin.

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arXiv - MATH - Commutative Algebra

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