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Let a $(g-1)$-dimensional complex abelian variety $P$ be a Prym variety of $C_f$ that corresponds to a unramified double cover of $C_f$. Suppose that there exists a subfield $K$ of $\\C$ such that $f(x)$ lies in $K[x]$, is irreducible over $K$ and its Galois group is the full symmetric group. Assuming that $g>2$, we prove that $End(P)$ is either the ring of integers $Z$ or the direct sum"},"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":"1012.3731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-16T19:58:29Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"d39353c7bcb4b4bdb4c7967c2ef88daf61bb9b8ae3c9aca1bcc0a97cad0265fc","abstract_canon_sha256":"9387b42ade76d8d7d9724bc6d2ca2b7aec2b954dce29b6134b3b66d2fe5824f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:05.741958Z","signature_b64":"Pm2wPKqV/Kze6ljSWg30IbWlE/8Myc6TF9SdMPWQ79nv2bKDd0nvtGdl/0txDlpY/HjnZGLNKDVx9YeAY9u7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3fb3b86bd17e93321d229810b3d27ebde31a35b7e1bc727c436d91a836caed3","last_reissued_at":"2026-05-18T04:33:05.741166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:05.741166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hodge classes on certain hyperelliptic prymians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Yuri G. 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Assuming that $g>2$, we prove that $End(P)$ is either the ring of integers $Z$ or the direct sum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3731","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":"1012.3731","created_at":"2026-05-18T04:33:05.741342+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.3731v1","created_at":"2026-05-18T04:33:05.741342+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3731","created_at":"2026-05-18T04:33:05.741342+00:00"},{"alias_kind":"pith_short_12","alias_value":"4P5TXBV5C7UT","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"4P5TXBV5C7UTGIOS","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"4P5TXBV5","created_at":"2026-05-18T12:26:04.259169+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/4P5TXBV5C7UTGIOSFGAQWPJH5P","json":"https://pith.science/pith/4P5TXBV5C7UTGIOSFGAQWPJH5P.json","graph_json":"https://pith.science/api/pith-number/4P5TXBV5C7UTGIOSFGAQWPJH5P/graph.json","events_json":"https://pith.science/api/pith-number/4P5TXBV5C7UTGIOSFGAQWPJH5P/events.json","paper":"https://pith.science/paper/4P5TXBV5"},"agent_actions":{"view_html":"https://pith.science/pith/4P5TXBV5C7UTGIOSFGAQWPJH5P","download_json":"https://pith.science/pith/4P5TXBV5C7UTGIOSFGAQWPJH5P.json","view_paper":"https://pith.science/paper/4P5TXBV5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.3731&json=true","fetch_graph":"https://pith.science/api/pith-number/4P5TXBV5C7UTGIOSFGAQWPJH5P/graph.json","fetch_events":"https://pith.science/api/pith-number/4P5TXBV5C7UTGIOSFGAQWPJH5P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4P5TXBV5C7UTGIOSFGAQWPJH5P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4P5TXBV5C7UTGIOSFGAQWPJH5P/action/storage_attestation","attest_author":"https://pith.science/pith/4P5TXBV5C7UTGIOSFGAQWPJH5P/action/author_attestation","sign_citation":"https://pith.science/pith/4P5TXBV5C7UTGIOSFGAQWPJH5P/action/citation_signature","submit_replication":"https://pith.science/pith/4P5TXBV5C7UTGIOSFGAQWPJH5P/action/replication_record"}},"created_at":"2026-05-18T04:33:05.741342+00:00","updated_at":"2026-05-18T04:33:05.741342+00:00"}