Intrinsic Approach to Galois Theory of 𝑞-Difference Equations

Abstract

The Galois theory of difference equations has witnessed a major evolution in the last two decades. In the particular case of q q -difference equations, authors have introduced several different Galois theories. In this memoir we consider an arithmetic approach to the Galois theory of q q -difference equations and we use it to establish an arithmetical description of some of the Galois groups attached to q q -difference systems.