{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3PYIDNS3IJLM5JJ7L53HERWQ34","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8a9dabbabbd336c97bc98a39af138c45d468aa338d1abcb052991dcbe17e13d5","cross_cats_sorted":["math.AG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-30T17:45:34Z","title_canon_sha256":"6abf704b37f0f9e3b07779d1f1d83f39a64d2c886c5da165b80129c96aa59b58"},"schema_version":"1.0","source":{"id":"1705.10769","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10769","created_at":"2026-05-18T00:43:23Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10769v1","created_at":"2026-05-18T00:43:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10769","created_at":"2026-05-18T00:43:23Z"},{"alias_kind":"pith_short_12","alias_value":"3PYIDNS3IJLM","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3PYIDNS3IJLM5JJ7","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3PYIDNS3","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:9aa63aa05b7bb56c30cc6ca4d514478ebaebb4e4f7e6b79daab7a07c61bf62d7","target":"graph","created_at":"2026-05-18T00:43:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $S$ be a finite dimensional noetherian scheme. For any proper morphism between smooth $S$-schemes, we prove a Riemann-Roch formula relating higher algebraic $K$-theory and motivic cohomology, thus with no projective hypothesis neither on the schemes nor on the morphism. We also prove, without projective assumptions, an arithmetic Riemann-Roch theorem involving Arakelov's higher $K$-theory and motivic cohomology as well as an analogue result for the relative cohomology of a morphism.\n  These results are obtained as corollaries of a motivic statement that is valid for morphisms between orien","authors_text":"A. Navarro, J. Navarro","cross_cats":["math.AG","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-30T17:45:34Z","title":"On the Riemann-Roch formula without projective hypothesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10769","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c1334968acbfd2fc1fe04ccebe56deb4025e6fd3a1f444d975171fb63eaf891b","target":"record","created_at":"2026-05-18T00:43:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8a9dabbabbd336c97bc98a39af138c45d468aa338d1abcb052991dcbe17e13d5","cross_cats_sorted":["math.AG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-30T17:45:34Z","title_canon_sha256":"6abf704b37f0f9e3b07779d1f1d83f39a64d2c886c5da165b80129c96aa59b58"},"schema_version":"1.0","source":{"id":"1705.10769","kind":"arxiv","version":1}},"canonical_sha256":"dbf081b65b4256cea53f5f767246d0df3fabfffaf0ddc92d029496596fccd920","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbf081b65b4256cea53f5f767246d0df3fabfffaf0ddc92d029496596fccd920","first_computed_at":"2026-05-18T00:43:23.553616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:23.553616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9mY55tvtwMWjLYfsO09h7e16/jqKsFqNcwoRggdDqLGDxwaCEpFOVQMpWSbNmQb2v0VoqmftmFn06F1pqM9uCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:23.554212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10769","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1334968acbfd2fc1fe04ccebe56deb4025e6fd3a1f444d975171fb63eaf891b","sha256:9aa63aa05b7bb56c30cc6ca4d514478ebaebb4e4f7e6b79daab7a07c61bf62d7"],"state_sha256":"a3904752e25a90191cd1b79405a2bae7048c9f74e3cbea70b13f1bbdcbe11fb5"}