Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some arithmetic properties of Weil polynomials of the form
  $t^{2g}+at^g+q^g$   An isogeny class $\mathcal{A}$ of abelian varieties defined over finite
fields is said to be "cyclic" if every variety in $\mathcal{A}$ has a cyclic
group of rational points. In this paper we study the local cyclicity of
Weil-central isogeny classes of abelian varieties, i.e. those with Weil
polynomials of the form $f_\mathcal{A}(t)=t^{2g}+at^g+q^g$, as well as the
local growth of the groups of rational points of the varieties in $\mathcal{A}$
after finite field extensions. We exploit the criterion: an isogeny class
$\mathcal{A}$ with Weil polynomial $f$ is cyclic if and only if $f'(1)$ is
coprime with $f(1)$ divided by its radical.

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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio