{"paper":{"title":"Infinitesimal K-theory","license":"","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Guillermo Corti\\~nas","submitted_at":"2000-01-25T17:18:16Z","abstract_excerpt":"In this paper we study the fiber F of the rational Jones-Goodwillie character $$ F:=\\hofiber(ch:K^\\rat(A)@>>>HN^\\rat(A)) $$ going from K-theory to negative cyclic homology of associative rings. We describe this fiber F in terms of sheaf cohomology. We prove that, for $n\\ge 1$, there is an isomorphism: $$ \\pi_n(F)\\cong H^{-n}_{inf}(A,K^\\rat) $$ between the homotopy of the fiber and the hypercohomology groups of $K^\\rat$ on a non-commutative version of Grothendieck's infinitesimal site."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0001138","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"}