{"paper":{"title":"Galois theory of quadratic rational functions with periodic critical points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.NT","authors_text":"\\\"Ozlem Ejder","submitted_at":"2024-01-26T13:42:27Z","abstract_excerpt":"Given a number field $k$, and a quadratic rational function $f(x) \\in k(x)$, the associated arboreal representation of the absolute Galois group of $k$ is a subgroup of the automorphism group of a regular rooted binary tree. Boston and Jones conjectured that the image of such a representation for $f \\in \\mathbb{Z}[x]$ contains a dense set of settled elements. An automorphism is settled if the number of its orbits on the $n\\text{th}$ level of the tree remains small as $n$ goes to infinity.\n  In this article, we exhibit many quadratic rational functions whose associated Arboreal Galois groups ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.14862","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/2401.14862/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"}