Bulletin de la societe mathematique de france vol:121 issue:4 pages:545-598
Let K be a finite extension of Q(p) and R its valuation ring. To any f is-an-element-of K[x], with x = (x1,..., x(n)), is associated Igusa's local zeta function Z(s) = integral-R(n)\f(x)\s\dx\, which is known to be meromorphic on C. The monodromy conjecture relates poles of Z(s) to eigenvalues of the (complex) monodromy of the hypersurface f = 0. Now we can express both a list of candidate-poles for Z(s) and the monodromy-eigenvalues in terms of certain numerical data of exceptional varieties, associated to an embedded resolution of f = 0. Using relations between those numerical data we study the vanishing of bad candidate-poles for Z(s) to obtain a lot of evidence for the conjecture.