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For each of the three quadratic extensions $K/k$ inside the absolute genus field $k^{(*)}$ of $k$, we compute the capitulation kernel of $K/k$. Then we deduce that each strongly ambiguous class of $k/Q(i)$ capitulates already in $k^{(*)}$."},"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":"1609.03087","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-10T20:48:56Z","cross_cats_sorted":[],"title_canon_sha256":"fa33a0faf2d021c61834958cbd861037e59dfd7c79afb2c5278177342c33aece","abstract_canon_sha256":"248781a8f6787e1af28dcb61d6085bcb2f76853d26a6e15555736b3bd990de8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:47.794291Z","signature_b64":"tbQIYrjmJXo4W19vam9tKlyTRP5RZWAMegBAog1BIkBiztnzRUTMgDuKxAKoHqMwr4vgjVICb+clmPYYDP2+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1919c1cbc1e7219a9b6bb8c11d98e14301c3e5efb03c1e58a83fda100364cbfd","last_reissued_at":"2026-05-18T01:04:47.793899Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:47.793899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Capitulation in the absolutely abelian extensions of some number fields II","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":"2016-09-10T20:48:56Z","abstract_excerpt":"We study the capitulation of $2$-ideal classes of an infinite family of imaginary biquadratic number fields consisting of fields $k =Q(\\sqrt{pq_1q_2}, i)$, where $i=\\sqrt{-1}$ and $q_1\\equiv q_2\\equiv-p\\equiv-1 \\pmod 4$ are different primes. For each of the three quadratic extensions $K/k$ inside the absolute genus field $k^{(*)}$ of $k$, we compute the capitulation kernel of $K/k$. 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