{"paper":{"title":"Patching and Quillen K-Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Patrick Mcfaddin","submitted_at":"2014-01-06T18:07:03Z","abstract_excerpt":"This paper provides an isomorphism $K_n (\\mathscr{A}) \\cong K_n (\\mathscr{A}_1) \\times_{K_n(\\mathscr{A}_0)} K_n(\\mathscr{A}_2)$ of $K$-groups, i.e., an exact sequence $0 \\to K_n(\\mathscr{A}) \\to K_n(\\mathscr{A}_1)\\times K_n(\\mathscr{A}_2) \\to K_n(\\mathscr{A}_0)$ corresponding to a 2-fiber product of abelian categories, taken with respect to exact functors. Using recent patching results of D. Harbater, J. Hartmann and D. Krashen, given fields $F_1, F_2 \\leq F_0$ and $F= F_1 \\cap F_2$ which satisfy a simple matrix factorization criterion, our isomorphism relates the $K$-groups of the fields $F$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1160","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"}