{"paper":{"title":"On automorphic points in polarized deformation rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Patrick B. Allen","submitted_at":"2016-01-14T21:12:05Z","abstract_excerpt":"For a fixed mod $p$ automorphic Galois representation, $p$-adic automorphic Galois representations lifting it determine points in universal deformation space. In the case of modular forms and under some technical conditions, B\\\"{o}ckle showed that every component of deformation space contains a smooth modular point, which then implies their Zariski density when coupled with the infinite fern of Gouv\\^{e}a-Mazur. We generalize B\\\"{o}ckle's result to the context of polarized Galois representations for CM fields, and to two dimensional Galois representations for totally real fields. More specific"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03752","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}