Local monodromy of constructible sheaves

Abstract Given a morphism f : X → S f\colon X\rightarrow S of complex algebraic varieties and a constructible sheaf 𝒢 on 𝑋, we compute the local monodromy of R ⁢ f ∗ ⁢ ( G ) Rf_{*}(\mathcal{G}) and R ⁢ f ! ⁢ ( G ) Rf_{!}(\mathcal{G}) in terms of the local monodromy of 𝒢. Our results generalize previous results by Brieskorn, Borel, Clemens, Deligne, Landman, Griffiths, Grothendieck, and Kashiwara in the setting of quasi-unipotent sheaves. In the following, we consider the general setting of sheaves of 𝑅-modules for a commutative noetherian ring 𝑅, and give applications to computing local monodromy of abelian covers in a uniform manner . We also obtain applications in the context of “generalized Alexander modules” and intersection cohomology with torsion coefficients.