Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A refined notion of arithmetically equivalent number fields, and curves
  with isomorphic Jacobians   We construct examples of number fields which are not isomorphic but for which
their idele class groups are isomorphic. We also construct examples of
projective algebraic curves which are not isomorphic but for which their
Jacobian varieties are isomorphic. Both are constructed using an example in
group theory provided by Leonard Scott of a finite group $G$ and subgroups
$H_1$ and $H_2$ which are not conjugate in $G$ but for which the $G$-module
${\mathbb Z}[G/H_1]$ is isomorphic to ${\mathbb Z}[G/H_2]$.

25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th