{"paper":{"title":"Kisin modules with descent data and parahoric local models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ana Caraiani, Brandon Levin","submitted_at":"2015-10-26T15:02:54Z","abstract_excerpt":"We construct a moduli space $Y^{\\mu, \\tau}$ of Kisin modules with tame descent datum $\\tau$ and with fixed $p$-adic Hodge type $\\leq \\mu$, for some finite extension $K/\\mathbb{Q}_p$. We show that this space is smoothly equivalent to the local model for $\\mathrm{Res}_{K/\\mathbb{Q}_p} \\mathrm{GL}_n$, cocharacter $\\{ \\mu \\}$, and parahoric level structure. We use this to construct the analogue of Kottwitz-Rapoport strata on the special fiber $Y^{\\mu, \\tau}$ indexed by the $\\mu$-admissible set. We also relate $Y^{\\mu, \\tau}$ to potentially crystalline Galois deformation rings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07503","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":""},"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"}