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Différentielles non commutatives et théorie de Galois différentielle ou aux différences

Yves André
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Abstract

We show how the Galois-Picard_Vessiot theory of differential equations and difference equations, and the theory of holonomy groups in differential geometry, are different aspects of a unique Galois theory. The latter is based upon the construction and study of the tensor product of non commutative connections over a commutative base, without any curvature assumption. This theory provides an algebraic frame for the study of the confluence arising when the increment of a difference equation tends to 0.

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Yves André. 2002-03-26. Différentielles non commutatives et théorie de Galois différentielle ou aux différences. https://arxiv.org/abs/math/0203274

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