{"paper":{"title":"$\\widehat{\\mathcal{D}}^{(0)}_{\\mathfrak{X}, k, \\mathbb{Q}}$-modules holonomes sur une courbe formelle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Raoul Hallopeau (IRMA)","submitted_at":"2022-08-29T12:07:52Z","abstract_excerpt":"Let $\\mathfrak{X}$ be a formal smooth curve over a complete discrete valuation ring $\\mathcal{V}$ of mixed characteristic $(0 , p)$. Let $\\widehat{\\mathcal{D}}^{(0)}_{\\mathfrak{X}, \\mathbb{Q}}$ be the sheaf of crystalline differential operators of level 0 (i.e., generated by the derivations). In this situation, Garnier proved that holonomic $\\widehat{\\mathcal{D}}^{(0)}_{\\mathfrak{X}, \\mathbb{Q}}$-modules as defined by Berthelot have finite length. In this article, we address this question for the sheaves $\\widehat{\\mathcal{D}}^{(0)}_{\\mathfrak{X}, k , \\mathbb{Q}}$ of congruence level $k$ defin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.14387","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.14387/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}