{"paper":{"title":"On Drinfeld's representability theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Drinfeld's representability theorem for moduli of p-divisible groups holds via a new transparent proof.","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Arnaud Vanhaecke","submitted_at":"2026-05-15T15:48:50Z","abstract_excerpt":"In the seventies, V. G. Drinfeld proved that a moduli problem of deformations by quasi-isogenies of certain $p$-divisible groups with extra actions is representable by an explicit semi-stable model of the $p$-adic symmetric space. This theorem, known as \\emph{Drinfeld's representability theorem}, has been one of the cornerstones of geometric aspects in $p$-adic Hodge theory. The purpose of these notes is twofold. On the one hand we give a new and more transparent proof of Drinfeld's representability theorem; on the other hand, we give a detailed presentation of Drinfeld's moduli space and the "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Drinfeld's representability theorem holds and admits a new, more transparent proof; the notes also supply a detailed presentation of Drinfeld's moduli space and the formal model of the p-adic symmetric space.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The moduli problem is defined exactly as the deformation problem by quasi-isogenies of certain p-divisible groups with extra actions that Drinfeld originally considered.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"New transparent proof of Drinfeld's representability theorem for moduli of p-divisible groups with extra actions, plus detailed presentation of the moduli space and formal model of the p-adic symmetric space.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Drinfeld's representability theorem for moduli of p-divisible groups holds via a new transparent proof.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7a86ef04f138b499b9be9ce022ef974379168a2d9fd997af95d2f087c74d2544"},"source":{"id":"2605.16092","kind":"arxiv","version":1},"verdict":{"id":"df5a953e-88e3-4e36-a7ba-bd0c3b7de8ef","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:42:46.817190Z","strongest_claim":"Drinfeld's representability theorem holds and admits a new, more transparent proof; the notes also supply a detailed presentation of Drinfeld's moduli space and the formal model of the p-adic symmetric space.","one_line_summary":"New transparent proof of Drinfeld's representability theorem for moduli of p-divisible groups with extra actions, plus detailed presentation of the moduli space and formal model of the p-adic symmetric space.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The moduli problem is defined exactly as the deformation problem by quasi-isogenies of certain p-divisible groups with extra actions that Drinfeld originally considered.","pith_extraction_headline":"Drinfeld's representability theorem for moduli of p-divisible groups holds via a new transparent proof."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16092/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.967610Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:51:45.262697Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:38.865986Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.496120Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"4d8cc87556133ec070ae443f359fbf97b9795b51795ca721ff99e4ef15c05395"},"references":{"count":66,"sample":[{"doi":"","year":2008,"title":"P. Abramenko and K. S. Brown.Buildings: Theory and applications. Grad. Texts Math. 248, Springer (2008)","work_id":"d6a7d514-5f37-4cba-8965-0a9fc4b1f9fb","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"T. Ahsendorf, C. Cheng, and T. Zink.O-displays andπ-divisible formalO-modules.J. Algebra, 457:129–193 (2016)","work_id":"a06d6db5-f33b-4eef-9d46-b6f190ae63e2","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"S. Bartling. The universal special formalO D-module ford= 2. Preprint, arXiv:2206.13195 (2022)","work_id":"ca0fb4b4-06fe-4093-8ab1-a3ce3631f8c6","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"S. Bartling and M. Hoff. Moduli spaces of nilpotent displays.Int. Math. Res. 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