Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Hasse principle for Shimura curves   Let C be an algebraic curve defined over a number field K, of positive genus
and without K-rational points. We conjecture that there exists some extension
field L over which C violates the Hasse principle, i.e., has points everywhere
locally but not globally. We show that our conjecture holds for all but
finitely many Shimura curves of the form X^D_0(N)_{/Q} or X^D_1(N)_{/Q}, where
D > 1 and N are coprime squarefree positive integers. The proof uses a
variation on a theorem of Frey, a gonality bound of Abramovich, and an analysis
of local points of small degree.

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The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
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The categories of this paper are: econ