Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniformity of stably integral points on principally polarized abelian
  surfaces   We prove, assuming that the conjecture of Lang and Vojta holds true, that
there is a uniform bound on the number of stably integral points in the
complement of the theta divisor on a principally polarized abelian surface
defined over a number field. This gives a uniform version, in the spirit of a
result of Caporaso-Harris-Mazur, of an unconditional theorem of Faltings. We
utilize recent results of Alexeev and Nakamura on complete moduli for
quasi-abelian varieties. We expect that a thorough understanding of current
work of Alexeev should give a more general result for abelian varieties of an
arbitrary dimension with a polarizing divisor of an arbitrary degree - a
proposed approach for such a generalization is given at the end of the paper.

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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph