{"paper":{"title":"The Moduli Stack of Breuil-Kisin Modules with Descent Data for Reductive Groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eivind Otto Hjelle","submitted_at":"2025-06-13T16:02:51Z","abstract_excerpt":"We introduce and study the moduli stack $\\mathcal{Y}$ of Breuil-Kisin modules with $\\hat{G}$-structure and descent data, or Breuil-Kisin $(\\Gamma,\\hat{G})$-torsors for short. Specifically, for a dominant cocharacter $\\mu$, we define the moduli stack $\\mathcal{Y}^{\\leq \\mu}$ of Breuil-Kisin $(\\Gamma,\\hat{G})$-torsors with Hodge-Tate weights bounded by $\\mu$. We prove that $\\mathcal{Y}^{\\leq \\mu}$ is a $p$-adic formal algebraic stack, and show that it is smoothly equivalent to (the $p$-adic completion of) a twisted Schubert variety $\\operatorname{Gr}^{\\leq \\mu}_{\\mathcal{G}}$ in the sense of Pap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11910","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/2506.11910/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"}