{"paper":{"title":"Good Reduction for Endomorphisms of the Projective Line in Terms of the Branch Locus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DS"],"primary_cat":"math.NT","authors_text":"J.K. Canci","submitted_at":"2015-05-19T20:15:48Z","abstract_excerpt":"Let $K$ be a number field and $v$ a non archimedean valuation on $K$. We say that an endomorphism $\\Phi\\colon \\mathbb{P}_1\\to \\mathbb{P}_1$ has good reduction at $v$ if there exists a model $\\Psi$ for $\\Phi$ such that $\\deg\\Psi_v$, the degree of the reduction of $\\Psi$ modulo $v$, equals $\\deg\\Psi$ and $\\Psi_v$ is separable. We prove a criterion for good reduction that is the natural generalization of a result due to Zannier in \\cite{Uz3}. Our result is in connection with other two notions of good reduction, the simple and the critically good reduction. The last part of our article is dedicate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05168","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"}