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.