{"paper":{"title":"Multiplicity one for the mod $p$ cohomology of Shimura curves: the tame case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Haoran Wang, Yongquan Hu","submitted_at":"2016-08-29T10:55:45Z","abstract_excerpt":"Let $F$ be a totally real field, $\\mathfrak{p}$ an unramified place of $F$ dividing $p$ and $\\overline{r}: \\mathrm{Gal}(\\overline{F}/F)\\rightarrow\\mathrm{GL}_2(\\overline{\\mathbb{F}}_p)$ a continuous irreducible modular representation. The work of Buzzard, Diamond and Jarvis associates to $\\overline{r}$ an admissible smooth representation of $\\mathrm{GL}_2(F_\\mathfrak{p})$ on the mod $p$ cohomology of Shimura curves attached to indefinite division algebras which split at $\\mathfrak{p}$. When $\\overline{r}|_{\\mathrm{Gal}(\\overline{F_\\mathfrak{p}}/F_\\mathfrak{p})}$ is tamely ramified and generic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07992","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"}