{"paper":{"title":"On the equation N_{K/k}(\\Xi)=P(t)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dasheng Wei","submitted_at":"2012-02-18T23:09:30Z","abstract_excerpt":"For varieties given by an equation N_{K/k}(\\Xi)=P(t), where N_{K/k} is the norm form attached to a field extension K/k and P(t) in k[t] is a polynomial, three topics have been investigated:\n  (1) computation of the unramified Brauer group of such varieties over arbitrary fields;\n  (2) rational points and Brauer-Manin obstruction over number fields (under Schinzel's hypothesis);\n  (3) zero-cycles and Brauer-Manin obstruction over number fields.\n  In this paper, we produce new results in each of three directions. We obtain quite general results under the assumption that K/k is abelian (as oppose"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4115","kind":"arxiv","version":3},"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"}