On D-cap-Modules of Finite Length on Rigid Analytic Spaces

Julian Reichardt

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arXiv · 2604.24173

On D-cap-Modules of Finite Length on Rigid Analytic Spaces

Julian Reichardt

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Abstract

We show that for quasi-compact smooth rigid analytic spaces, the extension functor sends holonomic D-modules to coadmissible D-cap-modules which are of finite length as weakly holonomic D-cap-modules. Using this, we show that the meromorphic connections considered by Bode--Bitoun and the local cohomology groups considered by Ardakov--Bode--Wadsley are of finite length as weakly holonomic D-cap-modules for quasi-compact smooth rigid analytic spaces. As a central tool, we introduce and study Hilbert polynomials for finitely generated modules over completed Weyl algebras.

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Julian Reichardt. 2026-07-14. On D-cap-Modules of Finite Length on Rigid Analytic Spaces. https://arxiv.org/abs/2604.24173

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