{"paper":{"title":"$p$-adic rigidity for $\\mathrm{GSp}_4$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Charlotte Clare-Hunt","submitted_at":"2026-07-02T23:08:05Z","abstract_excerpt":"This paper establishes the $p$-adic rigidity of certain suitably refined noncuspidal automorphic Saito$\\unicode{x2013}$Kurokawa representations of $\\mathrm{GSp}_4(\\mathbb{A}_\\mathbb{Q})$, in the sense that they cannot be interpolated in a nontrivial positive dimensional $p$-adic family. The results provide a $\\mathrm{GSp}_4$ analogue of Bella\\\"{i}che's rigidity theorems for $\\mathrm{U}(2,1)$ and identify an obstruction to $p$-adic variation on the $\\mathrm{GSp}_4$ eigenvariety."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02815","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/2607.02815/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"}