{"paper":{"title":"Infinite Hilbert Class Field Towers from Galois Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Cameron McLeman, Kirti Joshi","submitted_at":"2010-05-17T19:21:33Z","abstract_excerpt":"We investigate class field towers of number fields obtained as fixed fields of modular representations of the absolute Galois group of the rational numbers.  First, for each $k\\in\\{12,16,18,20,22,26\\}$, we give explicit rational primes $\\l$ such that the fixed field of the mod-$\\l$ representation attached to the unique normalized cusp eigenforms of weight $k$ on $\\Sl_2(\\Z)$ has an infinite class field tower.  Under a conjecture of Hardy and Littlewood, we further prove that there exist infinitely many such primes for each $k$ (in the above list).  Second, given a non-CM curve $E/\\Q$, we show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3003","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"}