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There is a unique ring morphism MGL^{2*,*}(k)--> Z which sends the class [X]_{MGL} of a smooth projective k-variety X to the Euler characteristic of the structure sheaf of X. Our main result states that there is a canonical grade preserving isomorphism of ring cohomology theories MGL^{*,*}(X,U) \\tensor_{MGL^{2*,*}(k)} Z --> K^{TT}_{- *}(X,U) = K'_{- *}(X-U)} on the category"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0709.4124","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-09-26T10:32:03Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"2cfa03c910bed88b49eaf6c1884a88ec000303d5c1327e9d1b39246e737ca29d","abstract_canon_sha256":"f3d74bcd11c75d9f6874c958c7484f00033acb1707f2049ba6e45a92146341d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:05:52.558019Z","signature_b64":"hyMXqg5YcshzKCFVwkvJTMAiHHLX8J0SuxHDVLNYwZBaZNKqaMEq608ckrawVCbQFIiBsRFtH2m+GNszsdF1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46f274f579835478baa05cbfbb2c7bff736a9efeeab0128479afb8ba0a99bba6","last_reissued_at":"2026-07-04T17:05:52.557633Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:05:52.557633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the relation of Voevodsky's algebraic cobordism to Quillen's K-theory","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"I. 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