{"paper":{"title":"Average Zsigmondy sets, dynamical Galois groups, and the Kodaira-Spencer map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Wade Hindes","submitted_at":"2016-03-14T20:28:19Z","abstract_excerpt":"Let $K$ be a global function field and let $\\phi\\in K[x]$. For all wandering basepoints $b\\in K$, we show that there is a bound on the size of the elements of the dynamical Zsigmondy set $\\mathcal{Z}(\\phi,b)$ that depends only on $\\phi$, the poles of the $b$, and $K$. Moreover, when we order $b\\in\\mathcal{O}_{K,S}$ by height, we show that $\\mathcal{Z}(\\phi,b)$ is empty on average. As an application, we prove that the inverse limit of the Galois groups of iterates of $\\phi(x)=x^d+f$ is a finite index subgroup of an iterated wreath product of cyclic groups. Finally, we establish similar results "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04459","kind":"arxiv","version":1},"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"}