{"paper":{"title":"Multivariable $(\\varphi,\\Gamma)$-modules and smooth $o$-torsion representations","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":"2015-11-03T19:17:22Z","abstract_excerpt":"Let $G$ be a $\\mathbb{Q}_p$-split reductive group with connected centre and Borel subgroup $B=TN$. We construct a right exact functor $D^\\vee_\\Delta$ from the category of smooth modulo $p^n$ representations of $B$ to the category of projective limits of finitely generated \\'etale $(\\varphi,\\Gamma)$-modules over a multivariable (indexed by the set of simple roots) commutative Laurent-series ring. These correspond to representations of a direct power of $\\mathrm{Gal}(\\overline{\\mathbb{Q}_p}/\\mathbb{Q}_p)$ via an equivalence of categories. Parabolic induction from a subgroup $P=L_PN_P$ correspond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01037","kind":"arxiv","version":4},"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"}