{"paper":{"title":"On the Distribution of Class Groups of Abelian Extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yuan Liu","submitted_at":"2024-11-28T18:43:36Z","abstract_excerpt":"Given a finite abelian group $\\Gamma$, we study the distribution of the $p$-part of the class group $\\operatorname{Cl}(K)$ as $K$ varies over Galois extensions of $\\mathbb{Q}$ or $\\mathbb{F}_q(t)$ with Galois group isomorphic to $\\Gamma$. We first construct a discrete valuation ring $e\\mathbb{Z}_p[\\Gamma]$ for each primitive idempotent $e$ of $\\mathbb{Q}_p[\\Gamma]$, such that 1) $e\\mathbb{Z}_p[\\Gamma]$ is a lattice of the irreducible $\\mathbb{Q}_p[\\Gamma]$-module $e\\mathbb{Q}_p[\\Gamma]$, and 2) $e\\mathbb{Z}_p[\\Gamma]$ is naturally a quotient of $\\mathbb{Z}_p[\\Gamma]$. For every $e$, we study t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19318","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/2411.19318/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"}