{"paper":{"title":"Hasse principle and weak approximation for multinorm equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Cyril Demarche, Dasheng Wei","submitted_at":"2012-12-24T10:18:29Z","abstract_excerpt":"In this note, we are interested in local-global principles for multinorm equations of the form $\\prod_{i=1}^n N_{L_i /k}(z_i) = a$ where $k$ is a global field, $L_i/k$ are finite separable field extensions and $a \\in k^*$.\n  In particular, we prove a result relating weak approximation for this equation to weak approximation for some classical norm equation $N_{F/k}(w) = a$ where $F := \\bigcap_{i=1}^n L_i$. It provides a proof of a \"weak approximation\" analogue of a recent conjecture by Pollio and Rapinchuk about multinorm principle. We also provide a counterexample to the original conjecture c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5889","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"}