Capitulation in the absolutely abelian extensions of some number fields II

2016/09/10 by Abdelmalek Azizi, Azizi, Abdelmalek, Abdelkader Zekhnini +3
Mathematics · #11R11 #11R16 #11R20 #11R27 #11R29 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11R11 #msc:11R16 #msc:11R20 #msc:11R27 #msc:11R29

paper · pdf · doi:10.48550/arxiv.1609.03087

17 pages, To be published by Acta Mathematica Vietnamica, 2016. arXiv admin note: substantial text overlap with arXiv:1507.00295, arXiv:1503.01992

arxiv created 2016/09/10 · arxiv updated 2016/09/13

Abstract

We study the capitulation of 2-ideal classes of an infinite family of imaginary biquadratic number fields consisting of fields k =Q(√(pq₁q₂), i), where i=√(-1) and q₁≡ q₂≡-p≡-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^(*).

Citations

• Capitulation in the absolutely abelian extensions of some fields ℚ(√(p₁p₂q), √(-1))
• On the strongly ambiguous classes of some biquadratic number fields

Related

• Capitulation in the absolutely abelian extensions of some fields ℚ(√(p₁p₂q), √(-1))
• On the strongly ambiguous classes of some biquadratic number fields
• Sur la capitulation des 2-classes d'idéaux du corps Q(√(2p₁p₂), i)
• Initial layer of the anti-cyclotomic ℤ₃-extension of ℚ(√(-m)) and capitulation phenomenon
• Capitulation, ambiguous classes and the cohomology of the units