{"paper":{"title":"On some notions of good reduction for endomorphisms of the projective line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Dajano Tossici, Giulio Peruginelli, Jung Kyu Canci","submitted_at":"2011-03-20T14:11:58Z","abstract_excerpt":"Let $\\Phi$ be an endomorphism of $\\SR(\\bar{\\Q})$, the projective line over the algebraic closure of $\\Q$, of degree $\\geq2$ defined over a number field $K$. Let $v$ be a non-archimedean valuation of $K$. We say that $\\Phi$ has critically good reduction at $v$ if any pair of distinct ramification points of $\\Phi$ do not collide under reduction modulo $v$ and the same holds for any pair of branch points. We say that $\\Phi$ has simple good reduction at $v$ if the map $\\Phi_v$, the reduction of $\\Phi$ modulo $v$, has the same degree of $\\Phi$. We prove that if $\\Phi$ has critically good reduction "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3853","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"}