{"paper":{"title":"A stacky approach to prismatic crystals via $q$-prism charts","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Zeyu Liu","submitted_at":"2025-04-09T16:24:51Z","abstract_excerpt":"Let $Y$ be a locally complete intersection over $\\mathcal{O}_K$ containing a $p$-power root of unity $\\zeta_p$. We classify the derived category of prismatic crystals on the absolute prismatic site of $Y$ by studying quasi-coherent complexes on the prismatization of $Y$ via $q$-prism charts. We also develop a Galois descent mechanism to remove the assumption on $\\mathcal{O}_K$. As an application, we classify quasi-coherent complexes on the Cartier-Witt stack and give a purely algebraic calculation of the cohomology of the structure sheaf on the absolute prismatic site of $\\mathbb{Z}_p$. Along "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.07005","kind":"arxiv","version":2},"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/2504.07005/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"}