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arXiv · 2004.01040

On quaternion algebras over some extensions of quadratic number fields

Vincenzo Acciaro·Diana Savin·Mohammed Taous·Abdelkader Zekhnini
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Abstract

Let $p$ and $q$ be two positive primes. Let $\ell$ be an odd positive prime integer and $F$ a quadratic number field. Let $K$ be an extension of $F$ such that $K$ is a dihedral extension of $\Q$ of degree $\ell$ over $F$ or $K$ is an abelian $\ell$-extension unramified over $F$ assuming $\ell$ divides the class number of $F$. In this paper, we obtain a complete characterization of division quaternion algebras $H_{K}(p, q)$ over $K$.

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Vincenzo Acciaro, Diana Savin, Mohammed Taous, Abdelkader Zekhnini. 2020-04-01. On quaternion algebras over some extensions of quadratic number fields. https://arxiv.org/abs/2004.01040

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