Abelian Varieties with Prescribed Embedding Degree

Details Abelian Varieties with Prescribed Embedding Degree Abelian Varieties with Prescribed Embedding Degree

2008-02-13

arxiv.org/abs/0802.1886v1

Mathematics

Number Theory

to appear in ANTS-VIII

Scientific paper

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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