Local Monodromy of constructible sheaves
Local Monodromy of constructible sheaves
Let听X听be a complex algebraic variety, and听X 脿听D听a proper morphism to a small disk which is smooth away from the origin. In this setting, the higher direct images of the constant sheaf form a local听system on the punctured disk, and the Local Monodromy听Theorem (due to Brieskorn-Grothendieck-Griffiths-Landsman) asserts that the eigenvalues of local monodromy are roots of unity. In this talk, we will discuss generalizations of this result to the setting of arbitrary morphisms between complex algebraic varieties, and with coefficients in arbitrary constructible sheaves. If there is time, I'll discuss applications to variation of monodromy听in abelian covers, and applications to the monodromy听of alexander modules. This is based on joint work with Madhav Nori.