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Let p be an odd prime, Z[\\zeta_p] the ring of integers in the p-th cyclotomic field,\n  C_{f,p}:y^p=f(x) the corresponding superelliptic curve and J(C_{f,p}) its jacobian. Assuming that either n=p+1 or p does not divide n(n-1), we prove that the ring of all endomorphisms of J(C_{f,p}) coincides with Z[\\zeta_p]."},"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":"math/0605028","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2006-04-30T21:23:35Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"8261c98851874eb060e03174de9d00829458a6a85f96861a671ae446aef3a8b3","abstract_canon_sha256":"53dd639f15d0d8602f4a63c847eaa8e62b93cbecdc8bb7e5b650bd0810236594"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:49.233198Z","signature_b64":"Sy/wpvN+aMfriBeev1qYzTHQnsi2oPHd2WIo62xpb2ToEkMwHJRjhIZV9DPk+B9GYknQrpa/+1wGwBHv4d0GDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d20120843ebb9aec344a8a49eb8522c2fd2117749061b03289e9d7658e386712","last_reissued_at":"2026-05-18T01:07:49.232743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:49.232743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Endomorphisms of superelliptic jacobians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Yuri G. Zarhin","submitted_at":"2006-04-30T21:23:35Z","abstract_excerpt":"Let K be a field of characteristic zero, n>4 an integer, f(x) an irreducible polynomial over K of degree n, whose Galois group is doubly transitive simple non-abelian group. Let p be an odd prime, Z[\\zeta_p] the ring of integers in the p-th cyclotomic field,\n  C_{f,p}:y^p=f(x) the corresponding superelliptic curve and J(C_{f,p}) its jacobian. Assuming that either n=p+1 or p does not divide n(n-1), we prove that the ring of all endomorphisms of J(C_{f,p}) coincides with Z[\\zeta_p]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605028","kind":"arxiv","version":6},"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":"math/0605028","created_at":"2026-05-18T01:07:49.232813+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0605028v6","created_at":"2026-05-18T01:07:49.232813+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605028","created_at":"2026-05-18T01:07:49.232813+00:00"},{"alias_kind":"pith_short_12","alias_value":"2IASBBB6XONO","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"2IASBBB6XONOYNCK","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"2IASBBB6","created_at":"2026-05-18T12:25:53.939244+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/2IASBBB6XONOYNCKRJE6XBJCYL","json":"https://pith.science/pith/2IASBBB6XONOYNCKRJE6XBJCYL.json","graph_json":"https://pith.science/api/pith-number/2IASBBB6XONOYNCKRJE6XBJCYL/graph.json","events_json":"https://pith.science/api/pith-number/2IASBBB6XONOYNCKRJE6XBJCYL/events.json","paper":"https://pith.science/paper/2IASBBB6"},"agent_actions":{"view_html":"https://pith.science/pith/2IASBBB6XONOYNCKRJE6XBJCYL","download_json":"https://pith.science/pith/2IASBBB6XONOYNCKRJE6XBJCYL.json","view_paper":"https://pith.science/paper/2IASBBB6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0605028&json=true","fetch_graph":"https://pith.science/api/pith-number/2IASBBB6XONOYNCKRJE6XBJCYL/graph.json","fetch_events":"https://pith.science/api/pith-number/2IASBBB6XONOYNCKRJE6XBJCYL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2IASBBB6XONOYNCKRJE6XBJCYL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2IASBBB6XONOYNCKRJE6XBJCYL/action/storage_attestation","attest_author":"https://pith.science/pith/2IASBBB6XONOYNCKRJE6XBJCYL/action/author_attestation","sign_citation":"https://pith.science/pith/2IASBBB6XONOYNCKRJE6XBJCYL/action/citation_signature","submit_replication":"https://pith.science/pith/2IASBBB6XONOYNCKRJE6XBJCYL/action/replication_record"}},"created_at":"2026-05-18T01:07:49.232813+00:00","updated_at":"2026-05-18T01:07:49.232813+00:00"}