Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The relative class number one problem for function fields, I   We classify finite extensions of function fields (of curves over finite
fields) with the same class number, except when both curves have base field
$\mathbb{F}_2$ and genus $>1$. In this case, we show that the zeta functions of
the curves form one of 208 explicit pairs, and find 64 examples of cyclic
extensions; the list is provably complete except if the base curve has genus 6
or 7 or if the extension is noncyclic. These cases will be resolved in
subsequent papers.

29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg