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The $E_2$-terms of this spectral sequence are the cdh-hypercohomology of a complex of equi-dimensional cycles.\n  Using this spectral sequence, we obtain a cycle class map from the relative motivic cohomology group of 0-cycles to the relative homotopy invariant K-theory. For a smooth scheme $X$ and a divisor $D \\subset X$, we construct a canonical homomorphism from the Chow groups with modulus $\\CH^i(X|D)$ to the relative motivic cohomology groups $H^{2i}(X|D, \\Z"},"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":"1801.00922","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-03T08:23:48Z","cross_cats_sorted":[],"title_canon_sha256":"af3851aeea214e9247bde2757d6f7f39587ff5f791f619cdacaa23140e092059","abstract_canon_sha256":"2683e1249e96fb877df07ea6bf3f7ae1e1c7319e63ba78595efb9192beba5678"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:34.244177Z","signature_b64":"hHE3onWYgGFXifPuGWdRKinHmOQJpAzS8K1iSE0HgMngVMrwDIheijcQAK/A5nxk0Bu79uvdYphcEK8nVqvYBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"688ad6b9af6d73b411f795b3ad236d9e64380827305b6928a1d9df424c0d3f35","last_reissued_at":"2026-05-17T23:51:34.243459Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:34.243459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Motivic spectral sequence for relative homotopy K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Amalendu Krishna, Pablo Pelaez","submitted_at":"2018-01-03T08:23:48Z","abstract_excerpt":"We construct a motivic spectral sequence for the relative homotopy invariant K-theory of a closed immersion of schemes $D \\subset X$. 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