The uniformizing Fuchsian lattice of a hyperbolic log-orbi curve is claimed to be reconstructed intrinsically as the Betti realization of a canonical maximal PSL2-Higgs object.
Opers with real monodromy and Eichler-Shimura isomorphism
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Uniformization as Tannakian Reconstruction
The uniformizing Fuchsian lattice of a hyperbolic log-orbi curve is claimed to be reconstructed intrinsically as the Betti realization of a canonical maximal PSL2-Higgs object.