{"paper":{"title":"A Dynamical N\\'eron--Ogg--Shafarevich Criterion via Orbital Arboreal Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DS","math.GR"],"primary_cat":"math.NT","authors_text":"J. Rogelio P\\'erez-Buend\\'ia","submitted_at":"2025-10-27T08:11:19Z","abstract_excerpt":"Let $K$ be a non-archimedean local field and $\\varphi : \\mathbb{P}^1 \\to \\mathbb{P}^1$ a rational endomorphism of degree $d \\geq 2$ over $K$. In the tame case ($p \\nmid d$), we show that strict good reduction is equivalent to the existence of a nonempty Zariski open subset $U_k \\subset \\mathbb{P}^1_k \\setminus \\mathrm{PC}(\\widetilde{\\varphi})$ over which the canonical residual morphism is finite \\'etale of degree $d$. The criterion separates two complementary local invariants of a normalized integral lift: $\\mathrm{Res}(F,G)$ controls residual degree drop, while the fiber discriminants $\\mathr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.23097","kind":"arxiv","version":3},"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/2510.23097/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"}