Poisson Geometry of the Moduli of Local Systems on Smooth Varieties

Abstract

We study the moduli of $G$-local systems on smooth but not necessarily proper complex algebraic varieties. We show that, when considered as derived algebraic stacks, they carry natural Poisson structures, generalizing the well-known case of curves. We also construct symplectic leaves of this Poisson structure by fixing local monodromies at infinity and show that a new feature, called strictness, appears as soon as the divisor at infinity has nontrivial crossings.