Title: Monodromy eigenvalues and zeta functions with differential forms Authors: Veys, Willem # × Issue Date: 2007 Publisher: Academic Press Series Title: Advances in mathematics vol:213 pages:341-357 Abstract: For a complex polynomial or analytic function f, there is a strong correspondence between poles of the so-called local zeta functions or complex powers \int |f|^{2s} \omega, where the \omega are C^\infty differential forms with compact support, and eigenvalues of the local monodromy of $f$. In particular Barlet showed that each monodromy eigenvalue of $f$ is of the form exp(2 \pi \sqrt{-1}s_0), where s_0 is such a pole. We prove an analogous result for similar p-adic complex powers, called Igusa (local) zeta functions, but mainly for the related algebro-geometric topological and motivic zeta functions. ISSN: 0001-8708 Publication status: published KU Leuven publication type: IT Appears in Collections: Algebra Section