Différentielles non commutatives et théorie de Galois différentielle ou aux différences

Details Différentielles non commutatives et théorie de Galois différentielle ou aux différences Différentielles non commutatives et théorie de Galois différentielle ou aux différences

2002-03-26

arxiv.org/abs/math/0203274v1

Annales Scient. \'Ec. Norm. Sup. 34 (2001), 685--739

Mathematics

General Mathematics

65 pages

Scientific paper

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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