Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reducible Abelian varieties and Lax matrices for Euler's problem of two
  fixed centres   Abel's quadratures for integrable Hamiltonian systems are defined up to a
group law of the corresponding Abelian variety $A$. If $A$ is isogenous to a
direct product of Abelian varieties $A\cong A_1\times\cdots\times A_k$, the
group law can be used to construct various Lax matrices on the factors
$A_1,\ldots,A_k$. As an example, we discuss 2-dimensional reducible Abelian
variety $A=E_+\times E_-$, which is a product of 1-dimensional varieties
$E_\pm$ obtained by Euler in his study of the two fixed centres problem, and
the Lax matrices on the factors $E_\pm$.

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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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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
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The categories of this paper are: chem-ph
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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: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ