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Non-abelian Hodge theory for algebraic curves in characteristic \(p\). (English) Zbl 1330.14015
Let \(C\) be a Riemann surface, and \(G_c\) be a compact Lie group with its complexification \(G\). In this case, one gets a bijection between stable \(G\)-Higgs bundles with vanishing Chern classes and irreducible \(G\)-local systems on \(C\). This is what C. T. Simpson called in [Publ. Math., Inst. Hautes Étud. Sci. 75, 5–95 (1992; Zbl 0814.32003)] the non-abelian Hodge theory for \(C\). In the present paper the authors try to establish the non-abelian Hodge theory in characteristic \(p>0\) in the following way. Let \(G\) be a reductive group over an algebraically closed field \(k\) of characteristic \(p\), and \(C\) be a smooth projective curve over \(k\) with \(C'\) its Frobenius twist. They give a description of the moduli space of flat \(G\)-bundles in terms of that of \(G\)-Higgs bundles over \(C'\).

MSC:
14D20 Algebraic moduli problems, moduli of vector bundles
14D23 Stacks and moduli problems
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
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