with Yves André. Astérisque 296(2004), 55--111. 
Abstract:
We present a p-adic theory of q-difference equations over arbitrarily thin annuli of outer radius 1. After a detailed study of rank one equations, we consider higher rank equations and prove a local monodromy theorem (a q-analog of Crew's quasi-unipotence conjecture). This allows us to define, in this context, a canonical functor of “confluence” from q-difference equations to differential equations, which turns out to be an equivalence of categories (in the presence of Frobenius structures).
About the proof of Proposition 2.7. Letter to Bernard Le Stum. (December 2nd, 2019)
Abstract:
This short note contains the details of the proof of Proposition 2.7 in the article above.