Différentielles non commutatives et théorie de Galois différentielle ou aux différences

2002/03/26 by Yves André
Mathematics · #math.GM #math.AC #math.QA #msc:12H05 #msc:12H10 #msc:12H20 #msc:13N05 #msc:13N10 #msc:34M15 #msc:81Q70 #msc:18D10 #msc:53C #msc:46L

paper · pdf

published as Annales Scient. Éc. Norm. Sup. 34 (2001), 685--739 · 65 pages

arxiv created 2002/03/26 · arxiv updated 2009/11/30

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.

Related

• Can we quantize Galois theory ?
• Toward quantized Picard-Vessiot theory, Further observations on our previous example
• A formulation of difference Galois theory
• On the Definitions of Difference Galois Groups
• Theorie De Galois Des Equations Differentielles