Différentielles non commutatives et théorie de Galois différentielle ou aux différences

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.