{"paper":{"title":"Finiteness of unramified deformation rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Frank Calegari, Patrick B. Allen","submitted_at":"2014-11-13T22:37:58Z","abstract_excerpt":"We prove that the universal unramified deformation ring $R^{\\mathrm{unr}}$ of a continuous Galois representation $\\overline{\\rho}: G_{F^{+}} \\rightarrow \\mathrm{GL}_n(k)$ (for a totally real field $F^{+}$ and finite field $k$) is finite over $\\mathcal{O} = W(k)$ in many cases. We also prove (under similar hypotheses) that the universal deformation ring $R^{\\mathrm{univ}}$ is finite over the local deformation ring $R^{\\mathrm{loc}}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3759","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":""},"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"}