Given a natural number and a log smooth integral morphism of fine log schemes of characteristic with a lifting of its Frobenius pull-back modulo , we use indexed algebras , of Lorenzon-Montagnon and the sheaf of log differential operators of level of Berthelot-Montagnon to construct an equivalence between the category of certain indexed -modules with -action and the category of certain indexed -modules with Higgs field. Our result is regarded as a level version of some results of Ogus-Vologodsky and Schepler.
Cite this article
Sachio Ohkawa, On logarithmic nonabelian Hodge theory of higher level in characteristic . Rend. Sem. Mat. Univ. Padova 134 (2015), pp. 47–91DOI 10.4171/RSMUP/134-2