{"paper":{"title":"On the cuspidal representations of ${\\rm GL}_2(F)$ of level 1 or 1/2 in the cohomology of the Lubin-Tate space $\\mathcal{X}(\\pi^2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Takahiro Tsushima, Tetsushi Ito, Yoichi Mieda","submitted_at":"2011-09-24T13:30:51Z","abstract_excerpt":"In this paper, we compute irreducible components which appear in the stable reduction of the Lubin-Tate curve of level two, in the mixed characteristic case.\n  We also compute the action of the central division algebra of invariant 1/2, the action of ${\\rm GL}_2$, and the inertia action explicitly. As a result, in a sense, we observe that, in the cohomology group of the stable reduction of the Lubin-Tate curve for ${\\rm GL}_2$, the local Langlands correspondence and the local Jacquet-Langlands correspondence for ${\\rm GL}_2$ are realized for the cuspidal representations of level 1 or 1/2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5265","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"}