Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recovering algebraic curves from L-functions of Hilbert class fields   In this paper, we prove that a smooth hyperbolic projective curve over a
finite field can be recovered from L-functions associated to the Hilbert class
field of the curve and its constant field extensions. As a consequence, we give
a new proof of a result of Mochizuki and Tamagawa that two such curves with
isomorphic fundamental groups are themselves isomorphic.

17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc