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

@article{PMIHES_2007__106__1_0,
     author = {Ogus, Arthur and Vologodsky, V.},
     title = {Nonabelian Hodge theory in characteristic $p$},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Springer},
     volume = {106},
     year = {2007},
     pages = {1-138},
     doi = {10.1007/s10240-007-0010-z},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_2007__106__1_0}
}
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/item/PMIHES_2007__106__1_0/

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