Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The prime divisors of the number of points on abelian varieties   Let A,A' be elliptic curves or abelian varieties fully of type GSp defined
over a number field K. This includes principally polarized abelian varieties
with geometric endomorphism ring Z and dimension 2 or odd. We compare the
number of points on the reductions of the two varieties. We prove that A and A'
are K-isogenous if the following condition holds for a density-one set of
primes p of K: the prime numbers dividing #A(k_p) also divide #A'(k_p). We
generalize this statement to some extent for products of such varieties. This
refines results of Hall and Perucca (2011) and of Ratazzi (2012).

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn