Topologization and Functional Analytification III

TL;DR

This paper advances the study of topologization and functional analytification within $al$-categorical and homotopical analytic geometry, focusing on prismatic cohomology and Robba stacks.

Contribution

It extends previous work by exploring prismatic cohomology and Robba stacks in the context of $al$-categorical and homotopical analytic geometry.

Findings

Development of prismatic cohomological constructions in this setting

Analysis of Robba stacks and sheaves in the $al$-categorical framework

Connections to recent advances by Bhatt-Lurie, Bhatt-Scholze, and Kedlaya-Liu

Abstract

In this paper, we continue our study on the topologization and functional analytification in $\infty$-categorical and homotopical analytic geometry. As in our previous articles on the $\infty$-categorical extensions of certain analytic and topological contexts, we discuss the corresponding prismatic cohomological constructions after Bhatt-Lurie, Bhatt-Scholze and Drinfeld, and the corresponding Robba stacks and sheaves after Kedlaya-Liu.