D-cap modules are quasi-coherent sheaves on an analytic stack

TL;DR

This paper establishes a deep connection between D-cap modules with Fréchet cohomology and quasi-coherent sheaves on an analytic stack, providing new descent results in the analytic topology.

Contribution

It constructs a fully-faithful functor linking D-cap modules to quasi-coherent sheaves and proves descent properties for these modules in the analytic setting.

Findings

Constructed a fully-faithful functor from D-cap modules to quasi-coherent sheaves.

Proved descent results for D-cap modules in the analytic topology.

Established foundational links between D-cap modules and sheaf theory on stacks.

Abstract

We construct a fully-faithful functor of $\infty$-categories from complexes of D-cap modules with Fr\'echet cohomology to quasi-coherent sheaves on an analytic stack. We prove various descent results for $\infty$-categories of D-cap modules in the analytic topology.