Computing the Galois group of a polynomial over a $p$-adic field

Christopher Doris

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arXiv · 2003.05834

Computing the Galois group of a polynomial over a $p$-adic field

Christopher Doris

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Abstract

We present a family of algorithms for computing the Galois group of a polynomial defined over a $p$-adic field. Apart from the "naive" algorithm, these are the first general algorithms for this task. As an application, we compute the Galois groups of all totally ramified extensions of $\mathbb{Q}_2$ of degrees 18, 20 and 22, tables of which are available online.

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Christopher Doris. 2020-03-12. Computing the Galois group of a polynomial over a $p$-adic field. https://arxiv.org/abs/2003.05834

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