{"paper":{"title":"Rationality of dynamical canonical height","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.DS","authors_text":"Dragos Ghioca, Laura DeMarco","submitted_at":"2016-02-17T22:17:33Z","abstract_excerpt":"We present a dynamical proof of the well-known fact that the Neron-Tate canonical height (and its local counterpart) takes rational values at points of an elliptic curve over a function field k of transcendence degree 1 over an algebraically closed field K of characteristic 0. More generally, we investigate the mechanism for which the local canonical height for a rational function f defined over k can take irrational values (at points in a local completion of k), providing examples in all degrees greater than 1. Building on Kiwi's classification of non-archimedean Julia sets for quadratic maps"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05614","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":""},"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"}