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We study the moduli of G-local systems on smooth but not necessarily propercomplex algebraic varieties. We show that, when suitably considered as derivedalgebraic stacks, they carry natural Poisson structures, generalizing the wellknown case of curves. We also construct symplectic leaves of this Poissonstructure by fixing local monodromies at infinity, and show that a new feature,called strictness, appears as soon as the divisor at infinity has non-trivialcrossings.

Poisson geometry of the moduli of local systems on smooth varieties