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Arthur Ogus

A Higgs Correspondence in Positive Characteristic

Abstract.

Carlos Simpson constructed an equivalence between the category of complex representations of the fundamental group of a complex projective manifold and the category of Higgs bundles (each subject to certain conditions). There is a similar correspondence for a smooth scheme in characteristic p, in which the category of complex representations is replaced by a suitable category of modules with integrable connection. This correspondence, (due to the expositor and Vologodsky) can be viewed as a "categori cation" of the Hodge-de Rham decomposition constructed by Deligne and Illusie, and serves as a "toy model" of the approach by Abbes and Gros to the construction of a p-adic Higgs correspondence.

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