{"paper":{"title":"Differential operators on locally analytic Shimura varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The locally analytic infinite-level Shimura variety can be fully reconstructed purely from its perfectoid counterpart and its B_dR^+-thickening via Grothendieck-Messing theory and a reformulated Riemann-Hilbert correspondence.","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Yuanyang Jiang","submitted_at":"2026-04-10T08:54:00Z","abstract_excerpt":"We investigate infinite-level Shimura varieties within the framework of analytic stacks of Clausen-Scholze, developing their smooth, completed, locally analytic, and de Rham realizations. We formulate a Grothendieck-Messing-Hodge-Tate period map, and establish a Grothendieck-Messing theory for locally analytic infinite-level Shimura varieties. This theory, combined with a reformulation of Riemann-Hilbert correspondence, implies that the locally analytic infinite-level Shimura variety can be fully reconstructed purely from its perfectoid counterpart and its $\\mathbb{B}_{\\mathrm{dR}}^{+}$-thicke"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The locally analytic infinite-level Shimura variety can be fully reconstructed purely from its perfectoid counterpart and its B_dR^+-thickening, via the Grothendieck-Messing theory combined with a reformulation of the Riemann-Hilbert correspondence.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the analytic stacks framework of Clausen-Scholze together with the reformulated Riemann-Hilbert correspondence actually produces a faithful reconstruction of the locally analytic Shimura variety from the perfectoid data and thickening.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Constructs differential operators and a BGG-Fontaine complex on locally analytic Shimura varieties, conjecturing automorphic properties after establishing a reconstruction theorem from perfectoid data.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The locally analytic infinite-level Shimura variety can be fully reconstructed purely from its perfectoid counterpart and its B_dR^+-thickening via Grothendieck-Messing theory and a reformulated Riemann-Hilbert correspondence.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"920585f4a4e3c65a7f4d56fe7ca56676325cb81561c25b3c09721ef9c2037390"},"source":{"id":"2604.09116","kind":"arxiv","version":2},"verdict":{"id":"d890f323-096f-424b-8e95-b05344297e0d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T17:03:35.610852Z","strongest_claim":"The locally analytic infinite-level Shimura variety can be fully reconstructed purely from its perfectoid counterpart and its B_dR^+-thickening, via the Grothendieck-Messing theory combined with a reformulation of the Riemann-Hilbert correspondence.","one_line_summary":"Constructs differential operators and a BGG-Fontaine complex on locally analytic Shimura varieties, conjecturing automorphic properties after establishing a reconstruction theorem from perfectoid data.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the analytic stacks framework of Clausen-Scholze together with the reformulated Riemann-Hilbert correspondence actually produces a faithful reconstruction of the locally analytic Shimura variety from the perfectoid data and thickening.","pith_extraction_headline":"The locally analytic infinite-level Shimura variety can be fully reconstructed purely from its perfectoid counterpart and its B_dR^+-thickening via Grothendieck-Messing theory and a reformulated Riemann-Hilbert correspondence."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.09116/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"}