Some split symbol algebras of prime degree

Diana Savin; Vincenzo Acciaro

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arXiv · 2003.03082

Some split symbol algebras of prime degree

Diana Savin·Vincenzo Acciaro

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Abstract

Let $p$ be an odd prime, let $K=\mathbb{Q}(ε)$ where $ε$ is a primitive cubic root of unity, and let $L$ be the Kummer field $\mathbb{Q}\left(ε, \sqrt[3]α\right)$. In this paper we obtain a characterization of the splitting behavior of the symbol algebras $\left( \frac{α,p}{K,ε}\right)$ and $\left( \frac{α,p^{h_{p}}}{K,ε}\right)$, where $h_{p}$ is the order in the class group $Cl\left(L\right)$ of a prime ideal of $\mathcal{O}_L$ which divides $p\mathcal{O}_L.$

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Diana Savin, Vincenzo Acciaro. 2020-12-27. Some split symbol algebras of prime degree. https://arxiv.org/abs/2003.03082

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