On D-cap-Modules of Finite Length on Rigid Analytic Spaces
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910168831229952 |
|---|---|
| author | Reichardt, Julian |
| author_facet | Reichardt, Julian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24173 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On D-cap-Modules of Finite Length on Rigid Analytic Spaces Reichardt, Julian Number Theory Algebraic Geometry 14G22 (Primary), 14F10, 16S32 (Secondary) 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. |
| title | On D-cap-Modules of Finite Length on Rigid Analytic Spaces |
| topic | Number Theory Algebraic Geometry 14G22 (Primary), 14F10, 16S32 (Secondary) |
| url | https://arxiv.org/abs/2604.24173 |