{"paper":{"title":"Vanishing of the Brauer group of a del Pezzo surface of degree 4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Manar Riman","submitted_at":"2019-07-20T13:35:25Z","abstract_excerpt":"We explicitly construct a del Pezzo surface $X$ of degree 4 over a field $k$ such that $\\operatorname{H}^1(k,\\operatorname{Pic}\\overline X)$ is isomorphic to $\\mathbb{ZZ}/2\\mathbb{Z}$ while $\\operatorname{Br} X/\\operatorname{Br} k$ is trivial. This proves that the algorithm to compute the Brauer group in [VAV] cannot be generalized in some cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08810","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"}