{"paper":{"title":"Ceresa cycles of bielliptic Picard curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Ari Shnidman, Jef Laga","submitted_at":"2023-12-20T12:08:46Z","abstract_excerpt":"We show that the Ceresa cycle $\\kappa(C_t)$ of the genus $3$ curve $C_t \\colon y^3 = x^4 + 2tx^2 + 1$ is torsion if and only if $Q_t=( \\sqrt[3]{t^2 -1},t)$ is a torsion point on the elliptic curve $y^2 = x^3 + 1$. This shows that there are infinitely many smooth plane quartic curves over $\\mathbb{C}$ (resp. $\\mathbb{Q}$) with torsion (resp. infinite order) Ceresa cycle. Over $\\overline{\\mathbb{Q}}$, we show that the Beilinson--Bloch height of $\\kappa(C_t)$ is proportional to the Neron--Tate height of $Q_t$. Thus, the height of $\\kappa(C_t)$ is nondegenerate and satisfies a Northcott property. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.12965","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.12965/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}