The monodromy conjecture for Bernstein–Sato polynomials of ideals

Let $X$ be a smooth affine variety, let $Z$ be a closed subscheme defined by an ideal $I\subset\mathcal O_X$, and let $x\in Z$. Write $b_I(s)$ and $b_{I,x}(s)$ for the global and local Bernstein–Sato polynomials, and $Z^{\operatorname{top}}_{X,Z}(s)$ and $Z^{\operatorname{top}}_{X,Z,x}(s)$ for the global and local topological zeta functions associated with $(X,Z)$. Monodromy conjecture. The products

$$b_I(s)\cdot Z^{\operatorname{top}}_{X,Z}(s)\quad\text{and}\quad b_{I,x}(s)\cdot Z^{\operatorname{top}}_{X,Z,x}(s)$$

have no poles. This is a version of the Monodromy Conjecture relating poles of topological zeta functions to roots of Bernstein–Sato polynomials for ideals.