{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OTWHFQEBFWAL4P7EPEJOHWWJNU","short_pith_number":"pith:OTWHFQEB","schema_version":"1.0","canonical_sha256":"74ec72c0812d80be3fe47912e3dac96d11941ad12dce2b7fab1051682a3cac08","source":{"kind":"arxiv","id":"1707.05049","version":1},"attestation_state":"computed","paper":{"title":"On the trace forms of Galois algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Baptiste Morin, Martin J. Taylor, Philippe Cassou-Nogu\\`es, Ted Chinburg","submitted_at":"2017-07-17T09:20:23Z","abstract_excerpt":"We study the trace form $q_L$ of $G$-Galois algebras $L/K$ when $G$ is a finite group and $K$ is a field of characteristic different from $2$. We introduce in this paper the category of $2$-reduced groups and, when $G$ is such a group, we use a formula of Serre to compute the second Hasse-Witt invariant of $q_L$. By combining this computation with work of Quillen we determine the isometry class of $q_L$ for large families of $G$-Galois algebras over global fields. We also indicate how our results generalize to Galois $G$-covers of schemes."},"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":"1707.05049","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-17T09:20:23Z","cross_cats_sorted":[],"title_canon_sha256":"9cefbcae00e7f8990d35e0b6fe77b7a28456cc1048da723bdc8c8b2131021e95","abstract_canon_sha256":"23607ccf33e018805fdb1840c696cb0f5c448985ab1ee2c76f0e5a628bffe6a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:11.500170Z","signature_b64":"zWJBP3kKCAn6ToWQrVHelmVaDpOiUKqeAQp6XX/WX273BWCZoBsjMH0XZKe8DUSk2j0l8q3JfUsgfyVeMgRtAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74ec72c0812d80be3fe47912e3dac96d11941ad12dce2b7fab1051682a3cac08","last_reissued_at":"2026-05-18T00:40:11.499682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:11.499682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the trace forms of Galois algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Baptiste Morin, Martin J. Taylor, Philippe Cassou-Nogu\\`es, Ted Chinburg","submitted_at":"2017-07-17T09:20:23Z","abstract_excerpt":"We study the trace form $q_L$ of $G$-Galois algebras $L/K$ when $G$ is a finite group and $K$ is a field of characteristic different from $2$. We introduce in this paper the category of $2$-reduced groups and, when $G$ is such a group, we use a formula of Serre to compute the second Hasse-Witt invariant of $q_L$. By combining this computation with work of Quillen we determine the isometry class of $q_L$ for large families of $G$-Galois algebras over global fields. We also indicate how our results generalize to Galois $G$-covers of schemes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05049","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1707.05049","created_at":"2026-05-18T00:40:11.499754+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.05049v1","created_at":"2026-05-18T00:40:11.499754+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05049","created_at":"2026-05-18T00:40:11.499754+00:00"},{"alias_kind":"pith_short_12","alias_value":"OTWHFQEBFWAL","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OTWHFQEBFWAL4P7E","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OTWHFQEB","created_at":"2026-05-18T12:31:34.259226+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/OTWHFQEBFWAL4P7EPEJOHWWJNU","json":"https://pith.science/pith/OTWHFQEBFWAL4P7EPEJOHWWJNU.json","graph_json":"https://pith.science/api/pith-number/OTWHFQEBFWAL4P7EPEJOHWWJNU/graph.json","events_json":"https://pith.science/api/pith-number/OTWHFQEBFWAL4P7EPEJOHWWJNU/events.json","paper":"https://pith.science/paper/OTWHFQEB"},"agent_actions":{"view_html":"https://pith.science/pith/OTWHFQEBFWAL4P7EPEJOHWWJNU","download_json":"https://pith.science/pith/OTWHFQEBFWAL4P7EPEJOHWWJNU.json","view_paper":"https://pith.science/paper/OTWHFQEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.05049&json=true","fetch_graph":"https://pith.science/api/pith-number/OTWHFQEBFWAL4P7EPEJOHWWJNU/graph.json","fetch_events":"https://pith.science/api/pith-number/OTWHFQEBFWAL4P7EPEJOHWWJNU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OTWHFQEBFWAL4P7EPEJOHWWJNU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OTWHFQEBFWAL4P7EPEJOHWWJNU/action/storage_attestation","attest_author":"https://pith.science/pith/OTWHFQEBFWAL4P7EPEJOHWWJNU/action/author_attestation","sign_citation":"https://pith.science/pith/OTWHFQEBFWAL4P7EPEJOHWWJNU/action/citation_signature","submit_replication":"https://pith.science/pith/OTWHFQEBFWAL4P7EPEJOHWWJNU/action/replication_record"}},"created_at":"2026-05-18T00:40:11.499754+00:00","updated_at":"2026-05-18T00:40:11.499754+00:00"}