The monodromy conjecture for motivic zeta functions of Calabi–Yau varieties

Let $K$ be a complete discretely valued field with algebraically closed residue field $k$, and let $X\to\operatorname{Spec}K$ be a smooth Calabi–Yau variety with volume form $\omega$. Let $Z_{X,\omega}(T)$ be its motivic zeta function, and let $q\in\mathbb{Q}$ be a pole. The tame monodromy operator acts on $H^*(X_{\overline{K}},\mathbb{Q}_l)$, where $l$ is prime to $\operatorname{char}k$. Monodromy conjecture. The number $e^{2\pi i q}$ is a monodromy eigenvalue. This conjecture predicts a direct relation between poles of motivic zeta functions and eigenvalues of the Galois-induced monodromy action; its status is not resolved in the supplied source.