{"paper":{"title":"On the Brauer-Manin obstruction for degree four del Pezzo surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Damaris Schindler, J\\\"org Jahnel","submitted_at":"2015-03-28T10:47:18Z","abstract_excerpt":"We show that, for every integer $1 \\leq d \\leq 4$ and every finite set $S$ of places, there exists a degree $d$ del Pezzo surface $X$ over ${\\mathbb Q}$ such that ${\\rm Br}(X)/{\\rm Br}({\\mathbb Q}) \\cong {\\mathbb Z}/2{\\mathbb Z}$ and the Brauer-Manin obstruction works exactly at the places in $S$. For $d = 4$, we prove that in all cases, with the exception of $S = \\{\\infty\\}$, this surface may be chosen diagonalizably over ${\\mathbb Q}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08292","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"}