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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1007.0665","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-07-05T12:11:42Z","cross_cats_sorted":[],"title_canon_sha256":"a4aa1d512fe24102d22a4880f31832d326cf2d400f17744090eaf301a28dd6d4","abstract_canon_sha256":"6ceee53abc1df0c8e7edbe44fc923213e4bbdb8af1e7bd78c1fa66de0b1ac8ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:19.694332Z","signature_b64":"kGTAlAUCpEUydM+zN58BqAriYHpCXwH7JRraqSc/EoJvc/B5HZy0LNR2Vlq6R6xPFWQDDAnldWlyyI827DosCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65fd54eeec05f36f4c85a4b81f3957bd3a92384def9cbb3fd3a0a4c294763bcb","last_reissued_at":"2026-05-17T23:53:19.693754Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:19.693754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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