Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twists of Shimura Curves   Consider a Shimura curve $X^D_0(N)$ over the rational numbers. We determine
criteria for the twist by an Atkin-Lehner involution to have points over a
local field. As a corollary we give a new proof of the theorem of
Jordan-Livn\'e on $\mathbf{Q}_p$ points when $p\mid D$ and for the first time
give criteria for $\mathbf{Q}_p$ points when $p\mid N$. We also give congruence
conditions for roots modulo $p$ of Hilbert class polynomials.

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The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
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The categories of this paper are: patt-sol
16
The categories of this paper are: stat
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The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg