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

Abstract

We will establish a nearby and vanishing cycle formalism for the arithmetic $\mathcal{D}$-module theory following Beilinson's philosophy. As an application, we define smooth objects in the framework of arithmetic $\mathcal{D}$-modules whose category is equivalent to the category of overconvergent isocrystals.

References in corpus (6)

• Semistable reduction for overconvergent F-isocrystals, III: Local semistable reduction at monomial valuations
• Relative log convergent cohomology and relative rigid cohomology I
• Theory of weights in p-adic cohomology
• Langlands correspondence for isocrystals and the existence of crystalline companions for curves
• Logarithmic $p$-bases and arithmetical differential modules
• Arithmetic D-modules on locally noetherian formal schemes