{"paper":{"title":"Operator ideals and assembly maps in $K$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.KT","authors_text":"Gisela Tartaglia, Guillermo Corti\\~nas","submitted_at":"2012-02-22T18:19:19Z","abstract_excerpt":"Let $\\cB$ be the ring of bounded operators in a complex, separable Hilbert space. For $p>0$ consider the Schatten ideal $\\cL^p$ consisting of those operators whose sequence of singular values is $p$-summable; put $\\cS=\\bigcup_p\\cL^p$. Let $G$ be a group and $\\vcyc$ the family of virtually cyclic subgroups. Guoliang Yu proved that the $K$-theory assembly map \\[ H_*^G(\\cE(G,\\vcyc),K(\\cS))\\to K_*(\\cS[G]) \\] is rationally injective. His proof involves the construction of a certain Chern character tailored to work with coefficients $\\cS$ and the use of some results about algebraic $K$-theory of ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4999","kind":"arxiv","version":3},"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"}