{"paper":{"title":"Generic smoothness for $G$-valued potentially semi-stable deformation rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rebecca Bellovin","submitted_at":"2014-03-06T11:31:50Z","abstract_excerpt":"We extend Kisin's results on the structure of characteristic $0$ Galois deformation rings to deformation rings of Galois representations valued in arbitrary connected reductive groups $G$. In particular, we show that such Galois deformation rings are complete intersection. In addition, we study explicitly the structure of the moduli space $X_{\\varphi,N}$ of (framed) $(\\varphi,N)$-modules when $G=\\GL_n$. We show that when $G=\\GL_3$ and $K_0=\\Q_p$, $X_{\\varphi,N}$ has a singular component, and we construct a moduli-theoretic resolution of singularities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1411","kind":"arxiv","version":2},"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"}