Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Artin pattern of heterogeneous multiplets of dihedral fields
  and proof of Scholz's conjecture   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.

35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con