{"paper":{"title":"Revisiting derived crystalline cohomology","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Zhouhang Mao","submitted_at":"2021-07-06T22:01:26Z","abstract_excerpt":"We prove that the $\\infty$-category of surjections of animated rings is projectively generated, introduce and study the notion of animated PD-pairs - surjections of animated rings with a \"derived\" PD-structure. This allows us to generalize classical results to non-flat and non-finitely-generated situations.\n  Using animated PD-pairs, we develop several approaches to derived crystalline cohomology and establish comparison theorems. As an application, we generalize the comparison between derived and classical crystalline cohomology from syntomic (affine) schemes (due to Bhatt) to quasisyntomic s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.02921","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/2107.02921/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"}