{"paper":{"title":"Criteria for p-ordinarity of families of elliptic curves over infinitely many number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nuno Freitas, Panagiotis Tsaknias","submitted_at":"2014-04-12T10:50:50Z","abstract_excerpt":"Let $K_i$ be a number field for all $i \\in \\mathbb{Z}_{> 0}$ and let $\\mathcal{E}$ be a family of elliptic curves containing infinitely many members defined over $K_i$ for all $i$. Fix a rational prime $p$. We give sufficient conditions for the existence of an integer $i_0$ such that, for all $i > i_0$ and all elliptic curve $E \\in \\mathcal{E}$ having good reduction at all $\\mathfrak{p} \\mid p$ in $K_i$, we have that $E$ has good ordinary reduction at all primes $\\mathfrak{p} \\mid p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3278","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"}