{"paper":{"title":"The imaginary case of the nonabelian Cohen--Lenstra heuristics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ken Willyard, Yuan Liu","submitted_at":"2025-07-29T07:43:49Z","abstract_excerpt":"For a finite group $\\Gamma$, we study the distribution of the Galois group $G_{\\emptyset}^{\\#}(K)$ of the maximal unramified extension of $K$ that is split completely at $\\infty$ and has degree prime to $|\\Gamma|$ and $\\textit{Char}(K)$, as $K$ varies over imaginary $\\Gamma$-extensions of $\\mathbb{Q}$ or $\\mathbb{F}_q(t)$. In the function field case, we compute the moments of the distribution of $G_{\\emptyset}^{\\#}(K)$ by counting points on Hurwitz stacks. In order to understand the probability of the distribution, we prove that $G_{\\emptyset}^{\\#}(K)$ admits presentations of a specific form, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.21558","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.21558/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"}