Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Capitulation in the absolutely abelian extensions of some number fields
  II   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
$K/k$. Then we deduce that each strongly ambiguous class of $k/Q(i)$
capitulates already in $k^{(*)}$.

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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph