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The aim of these notes is to generalize Laumon’s construction [20] of automorphic sheaves
corresponding to local systems on a smooth, projective curve to the case of local
systems with indecomposable unipotent ramification at a finite set of points. To this end
we need an extension of the notion of parabolic structure on vector bundles to coherent
sheaves. Once we have defined this, a lot of arguments from the article “ On the
geometric Langlands conjecture” by Frenkel, Gaitsgory and Vilonen [11]...
We take another approach to Hitchin’s strategy of computing the cohomology of moduli spaces of Higgs bundles by localization with respect to the circle action. Our computation is done in the dimensional completion of the Grothendieck ring of varieties and starts by describing the classes of moduli stacks of chains rather than their coarse moduli spaces. As an application we show that the -torsion of the Jacobian acts trivially on the middle dimensional cohomology of the moduli space of twisted...
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