{"paper":{"title":"On the rank of the fibers of elliptic K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Cecilia Salgado","submitted_at":"2013-07-15T15:36:10Z","abstract_excerpt":"Let $X$ be an elliptic K3 surface endowed with two distinct Jacobian elliptic fibrations $\\pi_i$, $i=1,2$, defined over a number field $k$. We prove that there is an elliptic curve $C\\subset X$ such that the generic rank over $k$ of $X$ after a base extension by $C$ is strictly larger than the generic rank of $X$. Moreover, if the generic rank of $\\pi_j$ is positive then there are infinitely many fibers of $\\pi_i$ ($j\\neq i$) with rank at least the generic rank of $\\pi_i$ plus one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3994","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"}