On the Azumaya algebra structure of the sheaf of log differential operators of higher level in positive characteristic...

In this talk, we explain the Azumaya algebra structure of the sheaf of log differential operators of higher level in prime characteristic. We also discuss about a splitting module of it under a certain liftability assumption modulo $p^{2}$. As a consequence, we obtain a Simpson type equivalence of categories in positive characteristic. Our 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.