Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Form class groups and class fields of CM-fields   Let $F$ be a totally real number field of class number one, and let $K$ be a
CM-field with $F$ as its maximal real subfield. For each positive integer $N$,
we construct a class group of certain binary quadratic forms over $F$ which is
isomorphic to the ray class group of $K$ modulo $N$. Assuming further that the
narrow class number of $F$ is one, we construct a class field of the reflex
field of $K$ in terms of the singular values of Hilbert modular functions.

11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc