Parabolic Hecke eigensheaves

Abstract

Following the strategy outlined in [DP09, DP22] for bundles of rank 2 on a smooth projective curve of genus 2, we construct flat connections over the moduli of stable bundles, with singularities along the wobbly locus. We verify that the associated Dmodules are Hecke eigensheaves. The local systems are constructed by the nonabelian Hodge correspondence from Higgs bundles. The spectral varieties of the Higgs bundles are the Hitchin fibers corresponding to the Hecke eigenvalues.