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We identify $C_f$ with the image of its canonical embedding into $J$ (the infinite point of $C_f$ goes to the zero of group law on $J$). It is known (arXiv:1809.03061 [math.AG]) that if $g>1$ then $C_f(K)$ does not contain torsion points, whose order lies between $3$ and $2g$.\n  In this paper we study torsion points of o"},"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":"1902.02743","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-07T17:39:39Z","cross_cats_sorted":[],"title_canon_sha256":"5d4356583c7a0402b15cc6bf48aae41dd034c9d1b10307b7bd74321b23c48ff0","abstract_canon_sha256":"31dda98bd8ece4e3e009fa268b2f9ecb179dd066c8444c3b2187ff229815955b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:39.047503Z","signature_b64":"fzHodWsAY8HJ4nR2f54N2xDK8GUiMPH0BxWtac514O2fzVgcRj6s8xP6t3wWB8YHPlTzxtrXGYIJxQw9Okp2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2dff901690ce75aa06fea84ad0d99cb5fa21c9188cccb6e56a2e5cb190a909c","last_reissued_at":"2026-05-17T23:40:39.047079Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:39.047079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Torsion Points of order 2g+1 on odd degree hyperelliptic curves of genus g","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Boris M. Bekker, Yuri G. Zarhin","submitted_at":"2019-02-07T17:39:39Z","abstract_excerpt":"Let $K$ be an algebraically closed field of characteristic different from $2$, $g$ a positive integer, $f(x)\\in K[x]$ a degree $2g+1$ monic polynomial without repeated roots, $C_f: y^2=f(x)$ the corresponding genus g hyperelliptic curve over $K$, and $J$ the jacobian of $C_f$. We identify $C_f$ with the image of its canonical embedding into $J$ (the infinite point of $C_f$ goes to the zero of group law on $J$). It is known (arXiv:1809.03061 [math.AG]) that if $g>1$ then $C_f(K)$ does not contain torsion points, whose order lies between $3$ and $2g$.\n  In this paper we study torsion points of o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02743","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":""},"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":"1902.02743","created_at":"2026-05-17T23:40:39.047143+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.02743v4","created_at":"2026-05-17T23:40:39.047143+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02743","created_at":"2026-05-17T23:40:39.047143+00:00"},{"alias_kind":"pith_short_12","alias_value":"4LP7SALJBTTV","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"4LP7SALJBTTVVIDP","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"4LP7SALJ","created_at":"2026-05-18T12:33:10.108867+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/4LP7SALJBTTVVIDP5KCK2DMZZN","json":"https://pith.science/pith/4LP7SALJBTTVVIDP5KCK2DMZZN.json","graph_json":"https://pith.science/api/pith-number/4LP7SALJBTTVVIDP5KCK2DMZZN/graph.json","events_json":"https://pith.science/api/pith-number/4LP7SALJBTTVVIDP5KCK2DMZZN/events.json","paper":"https://pith.science/paper/4LP7SALJ"},"agent_actions":{"view_html":"https://pith.science/pith/4LP7SALJBTTVVIDP5KCK2DMZZN","download_json":"https://pith.science/pith/4LP7SALJBTTVVIDP5KCK2DMZZN.json","view_paper":"https://pith.science/paper/4LP7SALJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.02743&json=true","fetch_graph":"https://pith.science/api/pith-number/4LP7SALJBTTVVIDP5KCK2DMZZN/graph.json","fetch_events":"https://pith.science/api/pith-number/4LP7SALJBTTVVIDP5KCK2DMZZN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4LP7SALJBTTVVIDP5KCK2DMZZN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4LP7SALJBTTVVIDP5KCK2DMZZN/action/storage_attestation","attest_author":"https://pith.science/pith/4LP7SALJBTTVVIDP5KCK2DMZZN/action/author_attestation","sign_citation":"https://pith.science/pith/4LP7SALJBTTVVIDP5KCK2DMZZN/action/citation_signature","submit_replication":"https://pith.science/pith/4LP7SALJBTTVVIDP5KCK2DMZZN/action/replication_record"}},"created_at":"2026-05-17T23:40:39.047143+00:00","updated_at":"2026-05-17T23:40:39.047143+00:00"}