{"paper":{"title":"Multivariable $(\\varphi,\\Gamma)$-modules and locally analytic vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Laurent Berger","submitted_at":"2013-12-17T12:41:51Z","abstract_excerpt":"Let $K$ be a finite extension of $\\mathbf{Q}_p$ and let $G_K = \\mathrm{Gal}(\\bar{\\mathbf{Q}}_p/K)$. There is a very useful classification of $p$-adic representations of $G_K$ in terms of cyclotomic $(\\varphi,\\Gamma)$-modules (cyclotomic means that $\\Gamma={\\rm Gal}(K_\\infty/K)$ where $K_\\infty$ is the cyclotomic extension of $K$). One particularly convenient feature of the cyclotomic theory is the fact that any $(\\varphi,\\Gamma)$-module is overconvergent.\n  Questions pertaining to the $p$-adic local Langlands correspondence lead us to ask for a generalization of the theory of $(\\varphi,\\Gamma)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4753","kind":"arxiv","version":8},"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"}