{"paper":{"title":"The prismatic realization functor for Shimura varieties of abelian type","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Alex Youcis, Hiroki Kato, Naoki Imai","submitted_at":"2023-10-12T16:29:38Z","abstract_excerpt":"For the integral canonical model $\\mathscr{S}_{\\mathsf{K}^p}$ of a Shimura variety $\\mathrm{Sh}_{\\mathsf{K}_0\\mathsf{K}^p}(\\mathbf{G},\\mathbf{X})$ of abelian type at hyperspecial level $K_0=\\mathcal{G}(\\mathbb{Z}_p)$, we construct a prismatic $F$-gauge model for the `universal' $\\mathcal{G}(\\mathbb{Z}_p)$-local system on $\\mathrm{Sh}_{\\mathsf{K}_0\\mathsf{K}^p}(\\mathbf{G},\\mathbf{X})$. We use this to obtain several new results about the $p$-adic geometry of Shimura varieties, notably an abelian-type analogue of the Serre--Tate deformation theorem (realizing an expectation of Drinfeld in the abe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.08472","kind":"arxiv","version":5},"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/2310.08472/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"}