{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6LDG3KF3FGIPNTG6AIRYRKVKWI","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":"b98bcec36b6fb9f77c1fbf59f8f7809b40e83f08a38e024813710aabc11e22a0","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-16T06:59:23Z","title_canon_sha256":"934648a84a5c3f8d98632bd9b61d47156a2143bf6a8e77c7de38ae0156062ab9"},"schema_version":"1.0","source":{"id":"1111.3718","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3718","created_at":"2026-05-18T04:08:13Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3718v1","created_at":"2026-05-18T04:08:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3718","created_at":"2026-05-18T04:08:13Z"},{"alias_kind":"pith_short_12","alias_value":"6LDG3KF3FGIP","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6LDG3KF3FGIPNTG6","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6LDG3KF3","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:d72620a19ac003863a0347e827f00ff0fa610774789c5fc6de7067470fc99b55","target":"graph","created_at":"2026-05-18T04:08:13Z","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":"Recently, Levine constructed a DG category whose homotopy category is equivalent to the full subcategory of motives over a base-scheme $S$ generated by the motives of smooth projective $S$-schemes, assuming that $S$ is itself smooth over a perfect field. In his construction, the tensor structure required $\\mathbb{Q}$-coefficients. The author has previously shown how to provide a tensor structure on the homotopy category mentioned above, when $S$ is semi-local and essentially smooth over a field of characteristic zero, extending Levine's tensor structure with $\\mathbb{Q}$-coefficients. In this ","authors_text":"Anandam Banerjee","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-16T06:59:23Z","title":"Tensor functor from Smooth Motives to motives over a base"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3718","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":"sha256:3022b17d7200716a70e706da742cae2b79f0b55cfccda4a5765316db0922d656","target":"record","created_at":"2026-05-18T04:08:13Z","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":"b98bcec36b6fb9f77c1fbf59f8f7809b40e83f08a38e024813710aabc11e22a0","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-16T06:59:23Z","title_canon_sha256":"934648a84a5c3f8d98632bd9b61d47156a2143bf6a8e77c7de38ae0156062ab9"},"schema_version":"1.0","source":{"id":"1111.3718","kind":"arxiv","version":1}},"canonical_sha256":"f2c66da8bb2990f6ccde022388aaaab220316565debfb1aa08bd145fea1f3421","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2c66da8bb2990f6ccde022388aaaab220316565debfb1aa08bd145fea1f3421","first_computed_at":"2026-05-18T04:08:13.193444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:13.193444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"USdz60gUyFy4OA0ko3kzW/jhZvI4qiJiisI1hzfI2vdaMUJDV4qH/whDGpLUHB8iJ3Ak3IC1nExiJ/ROGjACAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:13.194009Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.3718","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3022b17d7200716a70e706da742cae2b79f0b55cfccda4a5765316db0922d656","sha256:d72620a19ac003863a0347e827f00ff0fa610774789c5fc6de7067470fc99b55"],"state_sha256":"335ea2f4975f6f90c1a3da69aa691018fee09efd8dab2e94741068e4a9d2b3d7"}