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Published on Oct 6, 2014
In this talk, we construct a splitting module of the Azumaya algebra of log differential operators of higher level in characteristic 𝑝 greater than or equal 0 under the assumption of an existence of certain mod 𝑝2 lifting. As an application, we construct a Simpson type correspondence in characteristic 𝑝 greater than or equal 0. This result can be regarded as a generalization of the result of Ogus-Vologodsky and Gros-Le Stum-Quiros to the case of log schemes and that of Schepler to the case of higher level.