Iterative q difference Galois Theory

Abstract

We propose in this paper a Galois theory of $q$-difference equations where q is a root of unity. This theory is the q difference analogue of the Galois theory of iterative differential equations, that is differential equations over fields of positive characteristic. This theory contains and generalizes the Galois theory of q difference equations developed by Singer and van der Put.

to appear in "Journal fur die reine und angewandte Mathematik (Crelle's Journal)"