{"paper":{"title":"One-basedness and reductions of elliptic curves over real closed fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.LO","authors_text":"Davide Penazzi","submitted_at":"2012-08-03T10:48:06Z","abstract_excerpt":"Building on the positive solution of Pillay's conjecture we present a notion of \"intrinsic\" reduction for elliptic curves over a real closed field K. We compare such notion with the traditional algebro-geometric reduction and produce a classification of the group of K-points of an elliptic curve E with three \"real\" roots according to the way E reduces (algebro-geometrically) and the geometric complexity of the \"intrinsically\" reduced curve."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0708","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"}