Constructing Hecke eigensheaves via the Donagi-Pantev method: the case of genus 2 curves

Constructing Hecke eigensheaves via the Donagi-Pantev method: the case of genus 2 curves

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Carlos Simpson, Université de Nice

Zoom link:  https://princeton.zoom.us/j/91248028438

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We describe current work with R. Donagi and T. Pantev on the construction of Hecke eigensheaves over Bun_G entering into the geometric Langlands correspondence. Their method foresees the construction of parabolic Higgs sheaves with parabolic structure on the wobbly locus, then application of the nonabelian Hodge correspondence to get local systems on the complement of the wobbly locus. We are currently looking at the case of rank 2 bundles over a compact genus 2 curve. The construction may be viewed as an enhancement of their previous work on the classical limit. The Hecke property should follow from their abelianized Hecke property for the classical limit, this is a last point that is still work in progress.