{"paper":{"title":"Tame Galois module structure revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cornelius Greither, Fabio Ferri","submitted_at":"2018-05-31T17:55:03Z","abstract_excerpt":"A number field $K$ is Hilbert-Speiser if all of its tame abelian extensions $L/K$ admit NIB (normal integral basis). It is known that $\\mathbb{Q}$ is the only such field, but when we restrict $\\text{Gal}(L/K)$ to be a given group $G$, the classification of $G$-Hilbert-Speiser fields is far from complete. In this paper, we present new results on so-called $G$-Leopoldt fields. In their definition, NIB is replaced by ``weak NIB'' (defined below). Most of our results are negative, in the sense that they strongly limit the class of $G$-Leopoldt fields for some particular groups $G$, sometimes even "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12588","kind":"arxiv","version":3},"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"}