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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1507.00295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-01T17:41:09Z","cross_cats_sorted":[],"title_canon_sha256":"299743c3150f1d56c97ca07755231354a80727c00f24bc32be392d53b708b8bd","abstract_canon_sha256":"241226aedd539d326a74769dc826e9e84cdae51e884ce18ef4ea4850fcef4ba1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:29.286004Z","signature_b64":"8biFZZzjINm0o0OWnbOtQnWLqPeaew52EumF7EUxsszU8s8zuav/8wuLHn0EjbPFczO4gMxt/UaJq0Nbawp+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d88c3398c64631b11fc4e8a5e2d7262bd99258c1db87a1fe37a152c6ddbaad00","last_reissued_at":"2026-05-18T01:37:29.285259Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:29.285259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathbf{K}/\\mathbf{k}$. 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