Nonabelian Hodge theory in characteristic p
Publications Mathématiques de l'IHÉS, Volume 106 (2007), pp. 1-138.

Given a scheme in characteristic p together with a lifting modulo p 2 , we construct a functor from a category of suitably nilpotent modules with connection to the category of Higgs modules. We use this functor to generalize the decomposition theorem of Deligne-Illusie to the case of de Rham cohomology with coefficients.

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     author = {Ogus, A. and Vologodsky, V.},
     title = {Nonabelian {Hodge} theory in characteristic $p$},
     journal = {Publications Math\'ematiques de l'IH\'ES},
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     publisher = {Springer},
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     year = {2007},
     doi = {10.1007/s10240-007-0010-z},
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     url = {http://www.numdam.org/articles/10.1007/s10240-007-0010-z/}
}
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Ogus, A.; Vologodsky, V. Nonabelian Hodge theory in characteristic $p$. Publications Mathématiques de l'IHÉS, Volume 106 (2007), pp. 1-138. doi : 10.1007/s10240-007-0010-z. http://www.numdam.org/articles/10.1007/s10240-007-0010-z/

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