{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:5KNCINKXRY7WTO3PGFAD7N6VSY","short_pith_number":"pith:5KNCINKX","schema_version":"1.0","canonical_sha256":"ea9a2435578e3f69bb6f31403fb7d5960970696cded6ce4e25ed74860372b228","source":{"kind":"arxiv","id":"1411.4998","version":2},"attestation_state":"computed","paper":{"title":"Galois action on the homology of Fermat curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT"],"primary_cat":"math.NT","authors_text":"Kirsten Wickelgren, Rachel Davis, Rachel Pries, Vesna Stojanoska","submitted_at":"2014-11-18T20:20:34Z","abstract_excerpt":"In his paper titled \"Torsion points on Fermat Jacobians, roots of circular units and relative singular homology\", Anderson determines the homology of the degree $n$ Fermat curve as a Galois module for the action of the absolute Galois group $G_{\\mathbb{Q}(\\zeta_n)}$. In particular, when $n$ is an odd prime $p$, he shows that the action of $G_{\\mathbb{Q}(\\zeta_p)}$ on a more powerful relative homology group factors through the Galois group of the splitting field of the polynomial $1-(1-x^p)^p$. If $p$ satisfies Vandiver's conjecture, we prove that the Galois group of this splitting field over $"},"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":"1411.4998","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-18T20:20:34Z","cross_cats_sorted":["math.AG","math.AT"],"title_canon_sha256":"e65a87f45a24bbed4b09e64e9ad4bc040739ae7b7652caafbd05da4e981e63ec","abstract_canon_sha256":"5bf9c89a41ff7f785c3879ceaa14dd6fc640878ca63e5ed7dfb62e70e314de56"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:42.468942Z","signature_b64":"UcS84tATI5Eg1UxAq2HMMzDiJYP4fQOaAehTx+PfbzEj18iW3AFynGuQvfjHkt7WFSnoKQnPkObpxRzpVRp8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea9a2435578e3f69bb6f31403fb7d5960970696cded6ce4e25ed74860372b228","last_reissued_at":"2026-05-18T02:19:42.468514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:42.468514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Galois action on the homology of Fermat curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT"],"primary_cat":"math.NT","authors_text":"Kirsten Wickelgren, Rachel Davis, Rachel Pries, Vesna Stojanoska","submitted_at":"2014-11-18T20:20:34Z","abstract_excerpt":"In his paper titled \"Torsion points on Fermat Jacobians, roots of circular units and relative singular homology\", Anderson determines the homology of the degree $n$ Fermat curve as a Galois module for the action of the absolute Galois group $G_{\\mathbb{Q}(\\zeta_n)}$. In particular, when $n$ is an odd prime $p$, he shows that the action of $G_{\\mathbb{Q}(\\zeta_p)}$ on a more powerful relative homology group factors through the Galois group of the splitting field of the polynomial $1-(1-x^p)^p$. If $p$ satisfies Vandiver's conjecture, we prove that the Galois group of this splitting field over $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4998","kind":"arxiv","version":2},"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":"1411.4998","created_at":"2026-05-18T02:19:42.468576+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.4998v2","created_at":"2026-05-18T02:19:42.468576+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4998","created_at":"2026-05-18T02:19:42.468576+00:00"},{"alias_kind":"pith_short_12","alias_value":"5KNCINKXRY7W","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"5KNCINKXRY7WTO3P","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"5KNCINKX","created_at":"2026-05-18T12:28:14.216126+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/5KNCINKXRY7WTO3PGFAD7N6VSY","json":"https://pith.science/pith/5KNCINKXRY7WTO3PGFAD7N6VSY.json","graph_json":"https://pith.science/api/pith-number/5KNCINKXRY7WTO3PGFAD7N6VSY/graph.json","events_json":"https://pith.science/api/pith-number/5KNCINKXRY7WTO3PGFAD7N6VSY/events.json","paper":"https://pith.science/paper/5KNCINKX"},"agent_actions":{"view_html":"https://pith.science/pith/5KNCINKXRY7WTO3PGFAD7N6VSY","download_json":"https://pith.science/pith/5KNCINKXRY7WTO3PGFAD7N6VSY.json","view_paper":"https://pith.science/paper/5KNCINKX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.4998&json=true","fetch_graph":"https://pith.science/api/pith-number/5KNCINKXRY7WTO3PGFAD7N6VSY/graph.json","fetch_events":"https://pith.science/api/pith-number/5KNCINKXRY7WTO3PGFAD7N6VSY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5KNCINKXRY7WTO3PGFAD7N6VSY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5KNCINKXRY7WTO3PGFAD7N6VSY/action/storage_attestation","attest_author":"https://pith.science/pith/5KNCINKXRY7WTO3PGFAD7N6VSY/action/author_attestation","sign_citation":"https://pith.science/pith/5KNCINKXRY7WTO3PGFAD7N6VSY/action/citation_signature","submit_replication":"https://pith.science/pith/5KNCINKXRY7WTO3PGFAD7N6VSY/action/replication_record"}},"created_at":"2026-05-18T02:19:42.468576+00:00","updated_at":"2026-05-18T02:19:42.468576+00:00"}