Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On copies of the absolute Galois group in $\mathrm{Out}\hat{F}_2$   In this article we consider outer Galois actions on a free profinite group of
rank two, induced by the \'etale fundamental group of a projective line minus
three points or of a pointed elliptic curve over a number field. Under mild
technical assumptions their respective images uniquely determine the curves and
the number fields.

30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat