{"paper":{"title":"On $\\ell$-torsion in class groups of number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jordan Ellenberg, Lillian B. Pierce, Melanie Matchett Wood","submitted_at":"2016-06-20T13:07:27Z","abstract_excerpt":"For each integer $\\ell \\geq 1$, we prove an unconditional upper bound on the size of the $\\ell$-torsion subgroup of the class group, which holds for all but a zero-density set of field extensions of $\\mathbb{Q}$ of degree $d$, for any fixed $d \\in \\{2,3,4,5\\}$ (with the additional restriction in the case $d=4$ that the field be non-$D_4$). For sufficiently large $\\ell$ (specified explicitly), these results are as strong as a previously known bound that is conditional on GRH. As part of our argument, we develop a probabilistic \"Chebyshev sieve,\" and give uniform, power-saving error terms for th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06103","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":""},"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"}