{"paper":{"title":"Modular Chabauty: Effective S-Integral Point Computation On Curves with Elliptic Fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sa'ar Zehavi","submitted_at":"2025-05-19T10:35:00Z","abstract_excerpt":"We present a practical, unconditional algorithm for determining the $S$-integral points on any elliptic moduli problem $\\mathcal{Y}/\\mathbb{Z}[1/S]$ -- that is, on any geometrically connected curve carrying a non-isotrivial elliptic fibration $\\mathcal{E} \\to \\mathcal{Y}$. The associated map $\\Phi_M\\colon \\mathcal{Y} \\to \\mathcal{M}_{1,1}$ (the modular period map) plays the role ordinarily filled by a $p$-adic period map in Chabauty-type methods. Our Modular Chabauty method studies the image and fibres of $\\Phi_M$, and proceeds in two steps: an Effective Shafarevich step, in which we combine t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12947","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.12947/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"}