{"paper":{"title":"The Breuil--M\\'ezard conjecture for function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Zijian Yao","submitted_at":"2018-08-28T17:47:48Z","abstract_excerpt":"Let $K$ be a local function field of characteristic $l$, $\\mathbb{F}$ be a finite field over $\\mathbb{F}_p$ where $l \\ne p$, and $\\overline{\\rho}: G_K \\rightarrow \\text{GL}_n (\\mathbb{F})$ be a continuous representation. We apply the Taylor-Wiles-Kisin method over certain global function fields to construct a mod $p$ cycle map $\\overline{\\text{cyc}}$, from mod $p$ representations of $\\text{GL}_n (\\mathcal{O}_K)$ to the mod $p$ fibers of the framed universal deformation ring $R_{\\overline{\\rho}}^\\square$. This allows us to obtain a function field analog of the Breuil--M\\'ezard conjecture. Then "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09433","kind":"arxiv","version":1},"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"}