{"paper":{"title":"The Geometry of the Minimal Resultant Locus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Robert Rumely","submitted_at":"2014-02-24T23:42:00Z","abstract_excerpt":"Let K be a complete, algebraically closed, nonarchimedean valued field, and let f(z) be a rational function in K(z) of degree d at least 2. We show there is a natural way to assign non-negative integer weights w_f(P) to points of the Berkovich projective line over K, in such a way that the sum over all points is d-1. When f(z) has bad reduction, the set of points with nonzero weight forms a distributed analogue of the single point which occurs when f(z) has potential good reduction. Using this, we characterize the Minimal Resultant Locus of f(z) in dynamical and moduli-theoretic terms: dynamic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6017","kind":"arxiv","version":2},"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"}