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Rigid local systems over algebraic curves are those local systems determined by their local monodromies. They include many important classical local systems, such as those obtained from Bessel equatio...
These notes are based on lectures given at the Third International School on Geometry and Physics at the Centre de Recerca Matem`atica in Barcelona, March 26–30, 2012. The aim ofthe School’s four lect...
For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, ...
Abstract: Let S be a path-connected, locally-compact CW-complex, and let M be a subcomplex with finitely-many components. A `decorated SL_2(C)-local system' is an SL_2(C)-local system on S, together w...
Let X be a Hilbert modular variety and V a non-trivial local system over X. In this paper we study Deligne-Saito’s mixed Hodge structure (MHS) on the cohomology groups Hk(X, V) using the method of Hig...
For a simply connected solvable Lie group G with a cocompact discrete subgroup 􀀀, we consider the space of differential forms on the solvmanifold G/􀀀with values in certain flat bundl...

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