{"paper":{"title":"Finite ramification for preimage fields of postcritically finite morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alon Levy, Andrew Bridy, Jamie Juul, Joseph H. Silverman, Michelle Manes, Patrick Ingram, Rafe Jones, Simon Rubinstein-Salzedo","submitted_at":"2015-11-01T00:51:31Z","abstract_excerpt":"Given a finite endomorphism $\\varphi$ of a variety $X$ defined over the field of fractions $K$ of a Dedekind domain, we study the extension $K(\\varphi^{-\\infty}(\\alpha)) : = \\bigcup_{n \\geq 1} K(\\varphi^{-n}(\\alpha))$ generated by the preimages of $\\alpha$ under all iterates of $\\varphi$. In particular when $\\varphi$ is post-critically finite, i.e., there exists a non-empty, Zariski-open $W \\subseteq X$ such that $\\varphi^{-1}(W) \\subseteq W$ and $\\varphi : W \\to X$ is \\'etale, we prove that $K(\\varphi^{-\\infty}(\\alpha))$ is ramified over only finitely many primes of $K$. This provides a large"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00194","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"}