{"paper":{"title":"Potentially semi-stable deformation rings for discrete series extended types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sandra Rozensztajn","submitted_at":"2014-03-07T16:20:50Z","abstract_excerpt":"We define deformation rings for potentially semi-stable deformations of fixed discrete series inertial type in dimension $2$. In the case of representations of the Galois group of $\\mathbf{Q}_p$, we prove an analogue of the Breuil-M\\'ezard conjecture for these rings. As an application, we give some results on the existence of congruences modulo $p$ for newforms in $S_k(\\Gamma_0(p))$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1794","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"}