{"paper":{"title":"F-isocrystals of Higher Direct Images of $p$-Divisible Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yanshuai Qin, Zhenghui Li","submitted_at":"2025-06-13T12:47:12Z","abstract_excerpt":"For a $p$-divisible group $G$ over a smooth projective variety $X$ over $k$, where $k$ is a field finitely generated over a perfect field of characteristic $p$, we show that the formal group $R^i f_{\\fppf*} G$ is isogenous to a $p$-divisible group. The Dieudonn\\'e crystal of its divisible part is canonically isomorphic to the slope-$[0,1]$ part of $R^i f_{\\crys*} \\cM^{cr}(G)$ in the category of $F$-isocrystals over $k$. This provides an answer to the rational form of a question of Artin--Mazur regarding the enlarged formal Brauer groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11736","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/2506.11736/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"}