{"paper":{"title":"Capitulation in the absolutely abelian extensions of some fields $\\mathbb{Q}(\\sqrt{p_1p_2q}, \\sqrt{-1})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Abdelkader Zekhnini, Abdelmalek Azizi, Mohammed Taous","submitted_at":"2015-07-01T17:41:09Z","abstract_excerpt":"We study the capitulation of $2$-ideal classes of an infinite family of imaginary bicyclic biquadratic number fields consisting of fields $\\mathbf{k} =\\mathbb{Q}(\\sqrt{p_1p_2q}, i)$, where $i=\\sqrt{-1}$ and $p_1\\equiv p_2\\equiv-q\\equiv1 \\pmod 4$ are different primes. For each of the three quadratic extensions $\\mathbf{K}/\\mathbf{k}$ inside the absolute genus field $\\mathbf{k}^{(*)}$ of $\\mathbf{k}$, we compute the capitulation kernel of $\\mathbf{K}/\\mathbf{k}$. Then we deduce that each strongly ambiguous class of $\\mathbf{k}/\\mathbb{Q}(i)$ capitulates already in $\\mathbf{k}^{(*)}$, which is sm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00295","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"}