Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelian Varieties with Prescribed Embedding Degree   We present an algorithm that, on input of a CM-field $K$, an integer $k\ge1$,
and a prime $r \equiv 1 \bmod k$, constructs a $q$-Weil number $\pi \in \O_K$
corresponding to an ordinary, simple abelian variety $A$ over the field $\F$ of
$q$ elements that has an $\F$-rational point of order $r$ and embedding degree
$k$ with respect to $r$. We then discuss how CM-methods over $K$ can be used to
explicitly construct $A$.

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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th