{"paper":{"title":"Cutting towers of number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christian Maire, Farshid Hajir, Ravi Ramakrishna","submitted_at":"2019-01-14T14:58:44Z","abstract_excerpt":"Given a prime $p$, a number field $\\K$ and a finite set of places $S$ of $\\K$, let $\\K_S$ be the maximal pro-$p$ extension of $\\K$ unramified outside $S$. Using the Golod-Shafarevich criterion one can often show that $\\K_S/\\K$ is infinite. In both the tame and wild cases we construct infinite subextensions with bounded ramification using the refined Golod-Shafarevich criterion. In\n  the tame setting we achieve new records on Martinet constants (root discriminant bounds) in the totally real and totally complex cases.\n  We are also able to answer a question of Ihara by producing infinite asympto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04354","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"}