{"paper":{"title":"On D-cap-Modules of Finite Length on Rigid Analytic Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Holonomic D-modules extend to finite-length coadmissible D-cap-modules on quasi-compact smooth rigid analytic spaces.","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Julian Reichardt","submitted_at":"2026-04-27T08:32:01Z","abstract_excerpt":"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."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The rigid analytic spaces are quasi-compact and smooth, and the input D-modules are holonomic; the extension functor preserves the necessary coadmissibility and finite length properties under these conditions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Holonomic D-modules on quasi-compact smooth rigid analytic spaces extend to finite-length weakly holonomic D-cap-modules, with applications to meromorphic connections and local cohomology groups.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Holonomic D-modules extend to finite-length coadmissible D-cap-modules on quasi-compact smooth rigid analytic spaces.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"cd1abf58dd971f4bf62b69cd972b60918e6d70f743ebc84e593bd879f7e31bc1"},"source":{"id":"2604.24173","kind":"arxiv","version":2},"verdict":{"id":"badaf938-2ad0-4f03-a42e-207666098efe","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T01:47:21.138201Z","strongest_claim":"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","one_line_summary":"Holonomic D-modules on quasi-compact smooth rigid analytic spaces extend to finite-length weakly holonomic D-cap-modules, with applications to meromorphic connections and local cohomology groups.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The rigid analytic spaces are quasi-compact and smooth, and the input D-modules are holonomic; the extension functor preserves the necessary coadmissibility and finite length properties under these conditions.","pith_extraction_headline":"Holonomic D-modules extend to finite-length coadmissible D-cap-modules on quasi-compact smooth rigid analytic spaces."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.24173/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T07:36:33.164103Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:23:19.890540Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1f3416b8811b3afe9a78ad061cdae859c0911798713d7e3827cd50297cbd28e3"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}