  We prove that the cohomology jump loci of rank one local systems on the
complement in a small ball of a germ of a complex analytic set are finite
unions of torsion translates of subtori. This is a generalization of the
classical Monodromy Theorem stating that the eigenvalues of the monodromy on
the cohomology of the Milnor fiber of a germ of a holomorphic function are
roots of unity.

Algebraic Geometry;Algebraic Topology;Complex Variables