| Résume | The monodromy conjecture states that every pole of the topological (or related) zeta function of a polynomial f induces an eigenvalue of monodromy of f. This conjecture has already been studied a lot, but is in full generality proven only for zeta functions associated to polynomials in two variables. We consider a generalization, working with zeta functions associated to an ideal. First we present in arbitrary dimension a formula (like the one of A'Campo) to compute the Verdier monodromy eigenvalues associated to an ideal. This is used to prove a generalized monodromy conjecture for arbitrary ideals in two variables. |
