{"paper":{"title":"p-adic uniformization and the action of Galois on certain affine correspondences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Patrick Ingram","submitted_at":"2016-04-18T15:08:31Z","abstract_excerpt":"Given two monic polynomials f and g with coefficients in a number field K, and some a in K, we examine the action of the absolute Galois group of K on the directed graph of iterated preimages of a under the correspondence g(y)=f(x), assuming that deg(f)>deg(g) and that gcd(deg(f), deg(g))=1. If a prime of K exists at which f and g have integral coefficients, and at which a is not integral, we show that this directed graph of preimages consists of finitely many Galois-orbits. We obtain this result by establishing a p-adic uniformization of such correspondences, tenuously related to Bottcher's u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05197","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":""},"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"}