{"paper":{"title":"Tannakian twists of quadratic forms and orthogonal Nori motives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Baptiste Morin, Philippe Cassou-Nogu\\`es","submitted_at":"2015-11-10T08:48:16Z","abstract_excerpt":"We revisit classical results of Serre, Fr\\\"ohlich and Saito in the theory of quadratic forms. Given a neutral Tannakian category $(\\mathcal{T},\\omega)$ over a field $k$ of characteristic $\\neq 2$, another fiber functor $\\eta$ over a $k$-scheme $X$ and an orthogonal object $(M,q)$ in $\\mathcal{T}$, we show formulas relating the torsor $\\bf{Isom}^{\\otimes}(\\omega,\\eta)$ to Hasse-Witt invariants of the quadratic space $\\omega(M,q)$ and the symmetric bundle $\\eta(M,q)$. We apply this result to various neutral Tannakian categories arising in different contexts. We first consider Nori's Tannakian ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03022","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"}