  We study the moduli of G-local systems on smooth but not necessarily proper
complex algebraic varieties. We show that, when suitably 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 non-trivial
crossings.
