{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:IFF7CUH72SNGDG5TLQF4532ECI","short_pith_number":"pith:IFF7CUH7","schema_version":"1.0","canonical_sha256":"414bf150ffd49a619bb35c0bceef441218b1bef455964fc91c7170aa28fe98c2","source":{"kind":"arxiv","id":"2304.03539","version":4},"attestation_state":"computed","paper":{"title":"Witt groups of Severi-Brauer varieties and of function fields of conics","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Anne Qu\\'eguiner-Mathieu, Jean-Pierre Tignol","submitted_at":"2023-04-07T08:32:57Z","abstract_excerpt":"The Witt group of skew hermitian forms over a division algebra $D$ with symplectic involution is shown to be canonically isomorphic to the Witt group of symmetric bilinear forms over the Severi-Brauer variety of $D$ with values in a suitable line bundle. In the special case where $D$ is a quaternion algebra we extend previous work by Pfister and by Parimala on the Witt group of conics to set up two five-terms exact sequences relating the Witt groups of hermitian or skew-hermitian forms over $D$ with the Witt groups of the center, of the function field of the Severi-Brauer conic of $D$, and of "},"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":"2304.03539","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.KT","submitted_at":"2023-04-07T08:32:57Z","cross_cats_sorted":[],"title_canon_sha256":"bbab3d23dae26fb7ffbfd948eabbfb0f53ca06963f5dfb323dd38685e4eadbac","abstract_canon_sha256":"80b01497e622cd3ee4a80aa9ca9e2fea839ca6b3225e3f1f788c898a1cb156a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T14:03:16.466370Z","signature_b64":"p1IW3cU+mw1v4zBYX7cp/EJlrPQiK2s0eCWrPoZFu/VvTgPGXTgQt69TM4GxOtztRAcU/r3r5WuptlPX67AIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"414bf150ffd49a619bb35c0bceef441218b1bef455964fc91c7170aa28fe98c2","last_reissued_at":"2026-05-20T14:03:16.465949Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T14:03:16.465949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Witt groups of Severi-Brauer varieties and of function fields of conics","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Anne Qu\\'eguiner-Mathieu, Jean-Pierre Tignol","submitted_at":"2023-04-07T08:32:57Z","abstract_excerpt":"The Witt group of skew hermitian forms over a division algebra $D$ with symplectic involution is shown to be canonically isomorphic to the Witt group of symmetric bilinear forms over the Severi-Brauer variety of $D$ with values in a suitable line bundle. In the special case where $D$ is a quaternion algebra we extend previous work by Pfister and by Parimala on the Witt group of conics to set up two five-terms exact sequences relating the Witt groups of hermitian or skew-hermitian forms over $D$ with the Witt groups of the center, of the function field of the Severi-Brauer conic of $D$, and of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.03539","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.03539/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2304.03539","created_at":"2026-05-20T14:03:16.466007+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.03539v4","created_at":"2026-05-20T14:03:16.466007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.03539","created_at":"2026-05-20T14:03:16.466007+00:00"},{"alias_kind":"pith_short_12","alias_value":"IFF7CUH72SNG","created_at":"2026-05-20T14:03:16.466007+00:00"},{"alias_kind":"pith_short_16","alias_value":"IFF7CUH72SNGDG5T","created_at":"2026-05-20T14:03:16.466007+00:00"},{"alias_kind":"pith_short_8","alias_value":"IFF7CUH7","created_at":"2026-05-20T14:03:16.466007+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IFF7CUH72SNGDG5TLQF4532ECI","json":"https://pith.science/pith/IFF7CUH72SNGDG5TLQF4532ECI.json","graph_json":"https://pith.science/api/pith-number/IFF7CUH72SNGDG5TLQF4532ECI/graph.json","events_json":"https://pith.science/api/pith-number/IFF7CUH72SNGDG5TLQF4532ECI/events.json","paper":"https://pith.science/paper/IFF7CUH7"},"agent_actions":{"view_html":"https://pith.science/pith/IFF7CUH72SNGDG5TLQF4532ECI","download_json":"https://pith.science/pith/IFF7CUH72SNGDG5TLQF4532ECI.json","view_paper":"https://pith.science/paper/IFF7CUH7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.03539&json=true","fetch_graph":"https://pith.science/api/pith-number/IFF7CUH72SNGDG5TLQF4532ECI/graph.json","fetch_events":"https://pith.science/api/pith-number/IFF7CUH72SNGDG5TLQF4532ECI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IFF7CUH72SNGDG5TLQF4532ECI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IFF7CUH72SNGDG5TLQF4532ECI/action/storage_attestation","attest_author":"https://pith.science/pith/IFF7CUH72SNGDG5TLQF4532ECI/action/author_attestation","sign_citation":"https://pith.science/pith/IFF7CUH72SNGDG5TLQF4532ECI/action/citation_signature","submit_replication":"https://pith.science/pith/IFF7CUH72SNGDG5TLQF4532ECI/action/replication_record"}},"created_at":"2026-05-20T14:03:16.466007+00:00","updated_at":"2026-05-20T14:03:16.466007+00:00"}