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arXiv · 1904.06148

Generalized Artin pattern of heterogeneous multiplets of dihedral fields and proof of Scholz's conjecture

Daniel C. Mayer
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Abstract

The concept of Artin transfer pattern $((\ker(T_{K,N_i}))_i,(\mathrm{Cl}_p(N_i))_i)$ for homogeneous multiplets $(N_1,\ldots,N_m)$ of unramified cyclic prime degree p extensions $N_i/K$ of a base field K with p-class transfer homomorphisms$T_{K,N_i}:\,\mathrm{Cl}_p(K)\to\mathrm{Cl}_p(N_i)$ is generalized for heterogeneous multiplets of ramified extensions. By application to quadratic subfields K of dihedral fields N of degree 2p with an odd prime p, a conjecture of Scholz concerning the index of subfield units, $(U_N:U_0)$, for ramified extensions N/K with conductor f>1 is verified computationally.

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Daniel C. Mayer. 2019-04-12. Generalized Artin pattern of heterogeneous multiplets of dihedral fields and proof of Scholz's conjecture. https://arxiv.org/abs/1904.06148

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