{"paper":{"title":"(\\phi,\\Gamma)-modules over noncommutative overconvergent and Robba rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Gergely Z\\'abr\\'adi","submitted_at":"2012-08-16T12:05:11Z","abstract_excerpt":"We construct noncommutative multidimensional versions of overconvergent power series rings and Robba rings. We show that the category of \\'etale $(\\varphi,\\Gamma)$-modules over certain completions of these rings are equivalent to the category of \\'etale $(\\varphi,\\Gamma)$-modules over the corresponding classical overconvergent, resp. Robba rings (hence also to the category of $p$-adic Galois representations of $\\mathbb{Q}_p$). Moreover, in the case of Robba rings, the assumption of \\'etaleness is not necessary, so there exists a notion of trianguline objects in this sense."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3347","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"}