{"paper":{"title":"Finite index theorems for iterated Galois groups of cubic polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Andrew Bridy, Thomas J. Tucker","submitted_at":"2017-10-06T02:14:44Z","abstract_excerpt":"Let $K$ be a number field or a function field. Let $f\\in K(x)$ be a rational function of degree $d\\geq 2$, and let $\\beta\\in\\mathbb{P}^1(K)$. For all $n\\in\\mathbb{N}\\cup\\{\\infty\\}$, the Galois groups $G_n(\\beta)=\\text{Gal}(K(f^{-n}(\\beta))/K)$ embed into $\\text{Aut}(T_n)$, the automorphism group of the $d$-ary rooted tree of level $n$. A major problem in arithmetic dynamics is the arboreal finite index problem: determining when $[\\text{Aut}(T_\\infty):G_\\infty]<\\infty$. When $f$ is a cubic polynomial and $K$ is a function field of transcendence degree $1$ over an algebraic extension of $\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02257","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"}