{"paper":{"title":"Multivariable ({\\phi},{\\Gamma})-modules and products of Galois groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Gergely Z\\'abr\\'adi","submitted_at":"2016-03-14T12:14:44Z","abstract_excerpt":"We show that the category of continuous representations of the $d$th direct power of the absolute Galois group of $\\mathbb{Q}_p$ on finite dimensional $\\mathbb{F}_p$-vector spaces (resp. finitely generated $\\mathbb{Z}_p$-modules, resp. finite dimensional $\\mathbb{Q}_p$-vector spaces) is equivalent to the category of \\'etale $(\\varphi,\\Gamma)$-modules over a $d$-variable Laurent-series ring over $\\mathbb{F}_p$ (resp. over $\\mathbb{Z}_p$, resp. over $\\mathbb{Q}_p$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04231","kind":"arxiv","version":3},"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"}