{"paper":{"title":"Spinor Groups with Good Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrei S. Rapinchuk, Igor A. Rapinchuk, Vladimir I. Chernousov","submitted_at":"2017-07-25T16:05:52Z","abstract_excerpt":"Let $K$ be a 2-dimensional global field of characteristic $\\neq 2$, and let $V$ be a divisorial set of places of $K$. We show that for a given $n \\geqslant 5$, the set of $K$-isomorphism classes of spinor groups $G = \\mathrm{Spin}_n(q)$ of nondegenerate $n$-dimensional quadratic forms over $K$ that have good reduction at all $v \\in V$, is finite. This result yields some other finiteness properties, such as the finiteness of the genus $\\mathbf{gen}_K(G)$ and the properness of the global-to-local map in Galois cohomology. The proof relies on the finiteness of the unramified cohomology groups $H^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08062","kind":"arxiv","version":4},"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"}