{"paper":{"title":"Rigid character groups, Lubin-Tate theory, and $(\\varphi,\\Gamma)$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bingyong Xie, Laurent Berger, Peter Schneider","submitted_at":"2015-11-05T17:22:03Z","abstract_excerpt":"The construction of the $p$-adic local Langlands correspondence for $\\mathrm{GL}_2(\\mathbf{Q}_p)$ uses in an essential way Fontaine's theory of cyclotomic $(\\varphi,\\Gamma)$-modules. Here \\emph{cyclotomic} means that $\\Gamma = \\mathrm{Gal}(\\mathbf{Q}_p(\\mu_{p^\\infty})/\\mathbf{Q}_p)$ is the Galois group of the cyclotomic extension of $\\mathbf{Q}_p$. In order to generalize the $p$-adic local Langlands correspondence to $\\mathrm{GL}_2(L)$, where $L$ is a finite extension of $\\mathbf{Q}_p$, it seems necessary to have at our disposal a theory of Lubin-Tate $(\\varphi,\\Gamma)$-modules. Such a general"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01819","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"}