Capitulation in the absolutely abelian extensions of some fields ℚ(√(p₁p₂q), √(-1))

2015/07/01 by Abdelmalek Azizi, Azizi, Abdelmalek, Abdelkader Zekhnini +3
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #math.NT #msc:11R11 #msc:11R16 #msc:11R20 #msc:11R27 #msc:11R29 #msc:11R37

paper · pdf · doi:10.48550/arxiv.1507.00295

18 pages. arXiv admin note: substantial text overlap with arXiv:1503.01992

arxiv created 2015/07/01 · arxiv updated 2015/07/02

Abstract

We study the capitulation of 2-ideal classes of an infinite family of imaginary bicyclic biquadratic number fields consisting of fields k =ℚ(√(p₁p₂q), i), where i=√(-1) and p₁≡ p₂≡-q≡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. Then we deduce that each strongly ambiguous class of k/ℚ(i) capitulates already in k^(*), which is smaller than the relative genus field (k/ℚ(i))^*.

Citations

• On the strongly ambiguous classes of some biquadratic number fields

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