{"paper":{"title":"Brauer group of the moduli spaces of stable vector bundles of fixed determinant over a smooth curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Indranil Biswas, Tathagata Sengupta","submitted_at":"2018-04-07T02:47:33Z","abstract_excerpt":"Let $X$ be an irreducible smooth projective curve, defined over an algebraically closed field $k$, of genus at least three and $L$ a line bundle on $X$. Let ${\\mathcal M}_X(r,L)$ be the moduli space of stable vector bundles on $X$ of rank $r$ and determinant $L$ with $r\\geq 2$. We prove that the Brauer group ${\\rm Br}(\\mathcal{M}_X(r,L))$ is cyclic of order ${\\rm g.c.d.}(r,{\\rm degree}(L))$. We also prove that ${\\rm Br}(\\mathcal{M}_X(r,L))$ is generated by the class of the projective bundle obtained by restricting the universal projective bundle. These results were proved earlier in \\cite{BBGN"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02494","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"}