The Monodromy Conjecture for motivic zeta functions

Let $f\in \mathbb C[\bm x]\setminus \mathbb C$ and let $Z(f)$ denote its zero locus. For a region $W$ and the motivic zeta function $Z_{f,W}^{\mathrm{mot}}(s)$, let $b_f(s)$ be the Bernstein–Sato polynomial of $f$. A pole $s_0$ of $Z_{f,W}^{\mathrm{mot}}(s)$ is also required to satisfy the following two conditions.

Monodromy Conjecture. If $s_0$ is a pole of $Z_{f,W}^{\mathrm{mot}}(s)$, then $(s-s_0)\mid b_f(s)$, and $e^{s_0\cdot 2\pi \sqrt{-1}}$ is an eigenvalue of a local monodromy at some neighborhoods of points in $Z(f)\cap W$.

This conjecture connects poles of motivic zeta functions with roots of Bernstein–Sato polynomials and eigenvalues of local monodromy. Its status is not established by the supplied source context.