4 problems

A mixed function is a formal series … where $F$ is an $E$-function and $\mathfrak{f}$ is an arithmetic Gevrey function. For a non-anti-Stokes direction $\theta$, write…

Let $\mathfrak{f}(z)$ be an arithmetic Gevrey function and let $\theta\in(-\pi/2,\pi/2)$ satisfy $\mathfrak{f}_\theta(1)=0$. Division conjecture for arithmetic Gevrey functions. Th…

Gevrey-slope conjecture. The map $\beta\mapsto {\operatorname{d}_s}(A,\beta)$ is upper-semicontinuous. Moreover,

Let $X$ be a complex manifold, let $\rho_{\rm sa}$ denote the morphism from the subanalytic site of $X$ to $X$, and let $\rho_{\rm sa!}$, $\rho_{\rm sa}^{-1}$, and $\rho_{\rm sa*}$…