{"paper":{"title":"A predicted distribution for Galois groups of maximal unramified extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Zureick-Brown, Melanie Matchett Wood, Yuan Liu","submitted_at":"2019-07-11T05:31:33Z","abstract_excerpt":"We consider the distribution of the Galois groups $\\operatorname{Gal}(K^{\\operatorname{un}}/K)$ of maximal unramified extensions as $K$ ranges over $\\Gamma$-extensions of $\\mathbb{Q}$ or $\\mathbb{F}_q(t)$. We prove two properties of $\\operatorname{Gal}(K^{\\operatorname{un}}/K)$ coming from number theory, which we use as motivation to build a probability distribution on profinite groups with these properties. In Part I, we build such a distribution as a limit of distributions on $n$-generated profinite groups. In Part II, we prove as $q\\rightarrow\\infty$, agreement of $\\operatorname{Gal}(K^{\\op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05002","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.05002/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"}