Non-abelian Hodge theory for algebraic curves in characteristic p

Let G be a reductive group over an algebraically closed field of positive characteristic. Let C be a smooth projective curve over k. We give a description of the moduli space of flat G-bundles in terms of the moduli space of G-Higgs bundles over the Frobenius twist C' of C. This description can be regarded as the non-abelian Hodge theory for curves in positive characteristic.

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