Arithmetic D-modules on locally noetherian formal schemes

Abstract

We extend Berthelot's theory of arithmetic D-modules to a class of morphisms that are not necessarily of finite type. As an application we give a new construction of the category of convergent isocrystals on a separated scheme of finite type over a field, and show that the pullback by Frobenius is an auto-equivalence. This extends results of Berthelot that were proven in the smooth case.

arXiv comment82 pages. Comments welcome

Cited by in corpus (1)

• Around the nearby cycle functor for arithmetic $\mathcal{D}$-modules