{"paper":{"title":"The Borel-Moore homology of an arithmetic quotient of the Bruhat-Tits building of PGL of a non-archimedean local field in positive characteristic and modular symbols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Satoshi Kondo, Seidai Yasuda","submitted_at":"2014-06-27T00:08:10Z","abstract_excerpt":"We study the homology and the Borel-Moore homology with coefficients in $\\mathbb{Q}$ of a quotient (called arithmetic quotient) of the Bruhat-Tits building of $\\mathrm{PGL}$ of a nonarchimedean local field of positive characteristic by an arithmetic subgroup (a special case of the general definition in Harder's article (Invent.\\ Math.\\ 42, 135-175 (1977)).\n  We define an analogue of modular symbols in this context and show that the image of the canonical map from homology to Borel-Moore homology is contained in the sub $\\mathbb{Q}$-vector space generated by the modular symbols.\n  By definition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7047","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"}