{"paper":{"title":"Dynamique analytique sur $\\mathbf{Z}$. II : \\'Ecart uniforme entre Latt\\`es et conjecture de Bogomolov-Fu-Tschinkel","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"J\\'er\\^ome Poineau","submitted_at":"2022-07-04T16:52:03Z","abstract_excerpt":"We prove that the mutual energy (or the intersection product in the sense of Arakelov theory) of two dynamical systems associated to Latt\\`es morphisms over $\\mathbf{\\bar Q}$ is uniformly bounded below and deduce a proof of a conjecture of Bogomolov-Fu-Tschinkel: the number of common images of torsion points of two non-isomorphic elliptic curves over $\\mathbf{C}$ by a standard morphism to the projective line is uniformly bounded. The proof crucially relies on the theory of Berkovich spaces over $\\mathbf{Z}$ and on an original argument allowing to obtain a global estimate from a central estimat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.01574","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.01574/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}