{"paper":{"title":"Sur la capitulation des 2-classes d'id\\'eaux du corps Q(\\sqrt{2p_1p_2}, i)","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Abdelkader Zekhnini, Abdelmalek Azizi, Mohammed Taous","submitted_at":"2015-03-17T17:38:22Z","abstract_excerpt":"Let $p_1$ and $p_2$ be two primes such that $p_1\\equiv p_2\\equiv1 \\pmod4$ and at least two of the three elements $\\{(\\frac{2}{p_1}), (\\frac{2}{p_2}), (\\frac{p_1}{p_2})\\}$ are equal to -1. Put $i=\\sqrt{-1}$, $d=2p_1p_2$ and $k =Q(\\sqrt{d}, i)$. Let $k_2^{(1)}$ be the Hilbert 2-class field of $k$ and $k^{(*)}=Q(\\sqrt{p_1},\\sqrt{p_2},\\sqrt 2, i)$ be its genus field. Let $C_{k,2}$ denote the 2-part of the class group of $k$. The unramified abelian extensions of $k$ are $K_1=k(\\sqrt{p_1})$, $K_2=k(\\sqrt{p_2})$, $K_3=k(\\sqrt{2})$ and $k^{(*)}$. Our goal is to study the capitulation problem of the 2-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05132","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"}