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- W4293862033 abstract "For a fixed prime p, the p-class tower F(p,infinity,K) of a number field K is considered to be known if a pro-p presentation of the Galois group H = Gal( F(p,infinity,K)/K ) is given. In the last few years, it turned out that the Artin pattern AP(K) = (tau(K),kappa(K)) consisting of targets tau(K) = (Cl(p,L)) and kernels kappa(K) = (ker(J(L/K)) of class extensions J(L/K): Cl(p,K) --> Cl(p,L) to unramified abelian subfields L/K of the Hilbert p-class field F(p,1,K) only suffices for determining the two-stage approximation G = H/H of H. Additional techniques had to be developed for identifying the group H itself: searching strategies in descendant trees of finite p-groups, iterated and multilayered IPADs of second order, and the cohomological concept of Shafarevich covers involving relation ranks. This enabled the discovery of three-stage towers of p-class fields over quadratic base fields K = Q( squareroot(d) ) for p = 2,3,5. These non-metabelian towers reveal the new phenomenon of various tree topologies expressing the mutual location of the groups H and G." @default.
- W4293862033 created "2022-09-01" @default.
- W4293862033 creator A5025951707 @default.
- W4293862033 date "2016-05-31" @default.
- W4293862033 modified "2023-09-23" @default.
- W4293862033 title "Recent progress in determining p-class field towers" @default.
- W4293862033 doi "https://doi.org/10.48550/arxiv.1605.09617" @default.
- W4293862033 hasPublicationYear "2016" @default.
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