The Galois theory of difference equations has witnessed a major evolution during the past two decades, say Di Vizio and Hardouin, and in the particular case of q-difference equations, several different Galois theories have emerged. They consider here an arithmetic approach to the Galois theory of q-difference equations, and use it to establish an arithmetical description of some of the Galois groups attached to q-difference systems. After an introduction to q-difference equations, they cover the triviality of q-difference equations with rational coefficients, intrinsic Galois groups, and comparison with the non-linear theory. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)
