{"paper":{"title":"On the trace forms of Galois algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Baptiste Morin, Martin J. Taylor, Philippe Cassou-Nogu\\`es, Ted Chinburg","submitted_at":"2017-07-17T09:20:23Z","abstract_excerpt":"We study the trace form $q_L$ of $G$-Galois algebras $L/K$ when $G$ is a finite group and $K$ is a field of characteristic different from $2$. We introduce in this paper the category of $2$-reduced groups and, when $G$ is such a group, we use a formula of Serre to compute the second Hasse-Witt invariant of $q_L$. By combining this computation with work of Quillen we determine the isometry class of $q_L$ for large families of $G$-Galois algebras over global fields. We also indicate how our results generalize to Galois $G$-covers of schemes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05049","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"}