Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the torsion of Jacobians of principal modular curves of level 3^n   We demonstrate that the 3-power torsion points of the Jacobians of the
principal modular curves X(3^n) are fixed by the kernel of the canonical outer
Galois representation of the pro-3 fundamental group of the projective line
minus three points. The proof proceeds by demonstrating the curves in question
satisfy a two-part criterion given by Anderson and Ihara. Two proofs of the
second part of the criterion are provided; the first relies on a theorem of
Shimura, while the second uses the moduli interpretation.

22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
21
The categories of this paper are: adap-org