A few remarks on a Manin-Mumford conjecture in function field arithmetic and generalized Pila-Wilkie estimates

We present here the natural extension of our Pila-Wilkie type estimates on the number of rational points of the trascendent part of a compact analytic subset of ${\mathbb{F}}_q((1\mathrm{/}T){)}^n$ to analogous subsets of $K^n$, where $K$ is a general local field of any characteristic. That would integrate the analogous estimate provided by F. Loeser, G. Comte and R. Cluckers in characteristic 0.