$\infty$-Categorical Functional Analysis and $p$-adic Motives

Abstract

We discuss the deep relationship between ∞-categorical functional analysis and the anticipated theory of p-adic motives. The motivation fundamentally comes from applications essentially in arithmetics from very broad perspectives. The ∞-categorical homotopical aspects we considered here come mainly from Bambozzi-Ben-Bassat-Kremnizer, Ben-Bassat-Mukherjee, Bambozzi-Kremnizer, Clausen-Scholze and Kelly-Kremnizer-Mukherjee, based on deep robust foundation of ∞-categorical solids and ∞-categorical ind-Banach or bornological modules over general Banach rings.