{"paper":{"title":"Gauss sums, Jacobi sums and cyclotomic units related to torsion Galois modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Luca Caputo, St\\'ephane Vinatier","submitted_at":"2014-02-16T12:39:33Z","abstract_excerpt":"Let $G$ be a finite group and let $N/E$ be a tamely ramified $G$-Galois extension of number fields. We show how Stickelberger's factorization of Gauss sums can be used to determine the stable isomorphism class of various arithmetic $\\mathbb{Z}[G]$-modules attached to $N/E$. If $\\mathcal{O}_N$ and $\\mathcal{O}_E$ denote the rings of integers of $N$ and $E$ respectively, we get in particular that $\\mathcal{O}_N\\otimes_{\\mathcal{O}_E}\\mathcal{O}_N$ defines the trivial class in the class group $\\mathrm{Cl}(\\mathbb{Z}[G])$ and, if $N/E$ is also assumed to be locally abelian, that the square root of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3795","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"}