Cosheaf Theory and Overconvergent Verdier Duality for Rigid Analytic Spaces

TL;DR

This paper extends cosheaf theory to rigid analytic spaces and establishes a Verdier duality equivalence for overconvergent sheaves, paralleling classical topological results.

Contribution

It introduces a cosheaf framework for rigid analytic spaces and proves a Verdier duality theorem for overconvergent sheaves in this setting.

Findings

Established a sheaf-cosheaf Verdier duality for overconvergent sheaves

Extended cosheaf theory to rigid analytic spaces

Demonstrated an equivalence similar to classical Verdier duality

Abstract

This paper develops aspects of cosheaf theory on rigid analytic spaces, and demonstrates a sheaf-cosheaf Verdier duality equivalence theorem for overconvergent sheaves on separated, paracompact spaces, analogous to Jacob Lurie's treatment of Verdier duality for locally compact, Hausdorff topological spaces.