安德烈解代数的一般理论

IF 0.8 4区数学 Q2 MATHEMATICS

Annales De L Institut Fourier Pub Date : 2020-01-25 DOI:10.5802/AIF.3383

L. Nagy, Tam'as Szamuely

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引用次数: 4

摘要

我们将Yves Andre在微分伽罗瓦理论中的解代数理论推广到一般的Tannakian环境。作为应用，我们建立了具有正特征的迭代微分方程和差分方程的伽罗瓦群的解域与可观测子群对应关系的类似物。在差分代数环境中使用解代数也为超越理论中Philippon和Adamczewski—Faverjon的最新结果提供了新的途径。

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A general theory of André’s solution algebras

We extend Yves Andre's theory of solution algebras in differential Galois theory to a general Tannakian context. As applications, we establish analogues of his correspondence between solution fields and observable subgroups of the Galois group for iterated differential equations in positive characteristic and for difference equations. The use of solution algebras in the difference algebraic context also allows a new approach to recent results of Philippon and Adamczewski--Faverjon in transcendence theory.

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来源期刊

Annales De L Institut Fourier 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

1 months

期刊介绍： The Annales de l’Institut Fourier aim at publishing original papers of a high level in all fields of mathematics, either in English or in French. The Editorial Board encourages submission of articles containing an original and important result, or presenting a new proof of a central result in a domain of mathematics. Also, the Annales de l’Institut Fourier being a general purpose journal, highly specialized articles can only be accepted if their exposition makes them accessible to a larger audience.