{"paper":{"title":"A rational map with infinitely many points of distinct arithmetic degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"John Lesieutre, Matthew Satriano","submitted_at":"2018-08-31T20:25:24Z","abstract_excerpt":"Let $f \\colon X \\dashrightarrow X$ be a dominant rational self-map of a smooth projective variety defined over $\\overline{\\mathbb Q}$. For each point $P\\in X(\\overline{\\mathbb Q})$ whose forward $f$-orbit is well-defined, Silverman introduced the arithmetic degree $\\alpha_f(P)$, which measures the growth rate of the heights of the points $f^n(P)$. Kawaguchi and Silverman conjectured that $\\alpha_f(P)$ is well-defined and that, as $P$ varies, the set of values obtained by $\\alpha_f(P)$ is finite. Based on constructions of Bedford--Kim and McMullen, we give a counterexample to this conjecture wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00047","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"}