{"paper":{"title":"Some noncoherent, nonpositively curved K\\\"ahler groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.GT","authors_text":"Pierre Py","submitted_at":"2014-10-30T21:06:16Z","abstract_excerpt":"If $\\Gamma$ is any nonuniform lattice in the group ${\\rm PU}(2,1)$, let $\\overline{\\Gamma}$ be the quotient of $\\Gamma$ obtained by filling the cusps of $\\Gamma$ (i.e. killing the center of parabolic subgroups). Assuming that such a lattice $\\Gamma$ has positive first Betti number, we prove that for any sufficiently deep subgroup of finite index $\\Gamma_{1} < \\Gamma$, the group $\\overline{\\Gamma_{1}}$ is noncoherent. The proof relies on previous work of M. Kapovich as well as of C. Hummel and V. Schroeder."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8556","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"}