{"paper":{"title":"Self-Dual Integral Normal Bases and Galois Module Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Erik Jarl Pickett, St\\'ephane Vinatier","submitted_at":"2010-07-05T12:11:42Z","abstract_excerpt":"Let $N/F$ be an odd degree Galois extension of number fields with Galois group $G$ and rings of integers ${\\mathfrak O}_N$ and ${\\mathfrak O}_F=\\bo$ respectively. Let $\\mathcal{A}$ be the unique fractional ${\\mathfrak O}_N$-ideal with square equal to the inverse different of $N/F$. Erez has shown that $\\mathcal{A}$ is a locally free ${\\mathfrak O}[G]$-module if and only if $N/F$ is a so called weakly ramified extension. There have been a number of results regarding the freeness of $\\mathcal{A}$ as a $\\Z[G]$-module, however this question remains open. In this paper we prove that $\\mathcal{A}$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0665","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"}