Twisted calculus in several variables

In this paper, we introduce novel concepts and establish a formal framework for twisted differential operators in the context of several variables. The focus is on twisted coordinates within Huber rings, which facilitate the construction of diverse rings of twisted differential operators. We establish an equivalence between modules equipped with twisted connections and those endowed with an actions of twisted derivatives. Furthermore, we examine the convergence properties of twisted differential operators under specific conditions. This work aligns with the ongoing advancements, in $p$-adic Hodge cohomology and prismatic cohomology.