The local monodromy conjecture for topological zeta functions

Let $f:({\mathbb C}^{n+1},0)\to({\mathbb C},0)$ be a germ of an analytic function, and let $Z_{top,0}(f,s)\in{\mathbb Q}(s)$ be its local topological zeta function. A pole $s_0$ of this function is a candidate value associated with the local singularity. The local monodromy conjecture. If $s_0$ is a pole of $Z_{top,0}(f,s)$, then

$$\exp(2i\pi s_0)$$

is an eigenvalue of the local monodromy at some complex point of $f^{-1}(0)$. This connects poles of the topological zeta function with monodromy eigenvalues; the source presents it as a conjecture and does not state a resolution.