{"paper":{"title":"Zariski density of crystalline points on $\\GSp_{2n}$-valued local deformation rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kensuke Aoki","submitted_at":"2024-07-24T05:02:49Z","abstract_excerpt":"We introduce trianguline deformation spaces $X_{\\tri} (\\overline{\\rho})$ for a $\\GSp_{2n}$-valued residual representation $\\overline{\\rho} \\colon {\\mathcal{G}}_K \\to \\GSp_{2n} (k)$, where $k$ is a finite field of characteristic $p > 0$ and ${\\mathcal{G}}_K$ is the absolute Galois group of a finite extension $K / {\\mathbb{Q}}_p$, and study their properties. We show Zariski density of the crystalline points on the rigid generic fiber ${\\mathfrak{X}}_{\\overline{\\rho}}$ of the framed deformation space of $\\overline{\\rho}$ under some conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17005","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/2407.17005/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"}