{"paper":{"title":"The Brauer Group of a Surface over a Finite Field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yuri G. Zarhin","submitted_at":"2018-02-06T03:13:58Z","abstract_excerpt":"This is an English translation of the author's 1989 note in Russian, published in a collection \"Arithmetic and Geometry of Varieties\" (V.E. Voskresenski, ed.), Kuibyshev State University, Kuibyshev, 1989, pp. 57--67.\n  Let $X$ be be an absolutely irreducible smooth projective surface over a finite field $k$ of odd characteristic, let $Br(X)$ be the (commutative periodic) Brauer group of $X$ and $DIV Br(X)$ the subgroup of its divisible elements. We write $Br(X)_{DIV}$ for the quotient $Br(X)/DIV Br(X)$ and $Br(X)_{DIV}(2)$ for its (finite) $2$-primary component. We prove that the order of $Br("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01776","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"}