Denef–Loeser's topological monodromy conjecture

Let $h$ be a complex polynomial and let $Z_{\mathrm{top},0}(h,s)$ be its local topological zeta function at the origin. If $s_0$ is a pole, write it in the source's notation as $s_0=\nu+sN$. Denef–Loeser's topological monodromy conjecture. If $s_0=\nu+sN$ is a pole of $Z_{\mathrm{top},0}(h,s)$, then $\exp(2i\pi(-\nu/N))$ is an eigenvalue of the monodromy action at some point of $h^{-1}(0)$. This conjecture is a topological specialization of the motivic framework; the paper proves the motivic and topological monodromy conjectures for quasi-ordinary power series, but the general statement is not presented as solved.