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

中文翻译：

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围绕算术模块的附近循环函数

我们将为算术建立一个附近和消失的循环形式$\mathscr{D}$- 遵循贝林森哲学的模块理论。作为应用程序，我们在算术框架中定义平滑对象$\mathscr{D}$-模块，其类别等同于过收敛等晶的类别。