diffeomorphism $h_y: F_y \rightarrow F_y$ of the Milnor fiber, which is well-defined up to homotopy. This diffeomorphism in turn yields well-defined automorphisms of cohomology $M^k_y: H^k(F_y,{\mathbb C}) \rightarrow H^k(F_y, {\mathbb C})$ for all $k \geq 0$, called the *(local) monodromy transformations* of $f$ at $y$. An *eigenvalue of monodromy* or *monodromy eigenvalue* of $f$ (or of $Y$) is an eigenvalue of such a transformation $M^k_y$ for some $y \in Y$ and $k \geq 0$. It is well known that $H^k(F_y,{\mathbb C}) = 0$ for $k \geq n+1$ and that all monodromy eigenvalues are roots of unity. To investigate these monodromy eigenvalues, they are usually collected in the *zeta function of monodromy* or *monodromy zeta function* of $f$ at $y \in Y$ given by $$\label{eq:zeta-function-mon}
        Z_{f,y}^{mon}(t) = \prod_{k=0}^{n} \det(\text{Id} - tM^k_y)^{(-1)^k},$$ where $\text{Id}: H^k(F_y, {\mathbb C})\rightarrow H^k(F_y,{\mathbb C})$ is the identity. Denef [@Den2 Lemma 4.6] proved that every eigenvalue of monodromy of $f$ is a zero or pole of the monodromy zeta function of $f$ at some point $y \in Y$.

Unfortunately, this definition does not have a (straightforward) generalization to ideals. However, for one polynomial $f$, there is a more abstract description by Deligne [@De] using the notion of the 