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arXiv · 2002.00510

Hyperelliptic $\mathcal{S}_7$-curves of prime conductor

Armand Brumer·Kenneth Kramer
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Abstract

An abelian threefold $A_{/{\mathbb Q}}$ of prime conductor $N$ is favorable if its 2-division field $F$ is an ${\mathcal S}_7$-extension over ${\mathbb Q}$ with ramification index 7 over ${\mathbb Q}_2$. Let $A$ be favorable and let $B$ be a semistable abelian variety of dimension $3d$ and conductor $N^d$ with $B[2]$ filtered by copies of $A[2]$. We give a sufficient and computable class field theoretic criterion on $F$ to guarantee that $B$ is isogenous to $A^d$.

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Armand Brumer, Kenneth Kramer. 2020-02-02. Hyperelliptic $\mathcal{S}_7$-curves of prime conductor. https://arxiv.org/abs/2002.00510

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