{"paper":{"title":"The Breuil--M\\'{e}zard conjecture when $l \\neq p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jack Shotton","submitted_at":"2016-08-05T07:17:53Z","abstract_excerpt":"Let $l$ and $p$ be primes, let $F/\\mathbb{Q}_p$ be a finite extension with absolute Galois group $G_F$, let $\\mathbb{F}$ be a finite field of characteristic $l$, and let $\\bar{\\rho} : G_F \\rightarrow GL_n(\\mathbb{F})$ be a continuous representation. Let $R^\\square(\\bar{\\rho})$ be the universal framed deformation ring for $\\bar{\\rho}$. If $l = p$, then the Breuil--M\\'{e}zard conjecture (as formulated by Emerton and Gee) relates the mod $l$ reduction of certain cycles in $R^\\square(\\bar{\\rho})$ to the mod $l$ reduction of certain representations of $GL_n(\\mathcal{O}_F)$. We state an analogue of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01784","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"}