{"paper":{"title":"Prismatic crystals and $p$-adic Riemann--Hilbert correspondence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Hui Gao, Yu Min, Yupeng Wang","submitted_at":"2024-11-27T22:09:21Z","abstract_excerpt":"We systematically study relative and absolute ${\\Delta}_{\\mathrm{dR}}^+$-crystals on the (log-) prismatic site of a smooth (resp.~ semi-stable) formal scheme. Using explicit computation of stratifications, we classify (local) relative crystals by certain nilpotent connections, and classify (local) absolute crystals by certain enhanced connections. By using a $p$-adic Riemann--Hilbert functor and an infinite dimensional Sen theory over the Kummer tower, we globalize the results on absolute crystals and further classify them by certain small (global) $\\mathbb{B}_{\\mathrm{dR}}^+$-local systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18780","kind":"arxiv","version":1},"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/2411.18780/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"}