{"paper":{"title":"Insufficiency of the \\'etale Brauer-Manin obstruction: towards a simply connected example","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Arne Smeets","submitted_at":"2014-09-23T19:23:58Z","abstract_excerpt":"Since Poonen's construction of a variety $X$ defined over a number field $k$ for which $X(k)$ is empty and the \\'etale Brauer--Manin set $X(\\mathbf{A}_k)^\\text{Br,et}$ is not, several other examples of smooth, projective varieties have been found for which the \\'etale Brauer--Manin obstruction does not explain the failure of the Hasse principle. All known examples are constructed using \"Poonen's trick\", i.e. they have the distinctive feature of being fibrations over a higher genus curve; in particular, their Albanese variety is non-trivial.\n  In this paper, we construct examples for which the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6706","kind":"arxiv","version":2},"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"}