If $K$ is a finite extension of $\mathbb{Q}_p$, then let $\mathcal{O}_K$ denote its ring of integers. Let $P$ be its unique maximal ideal. Then $\mathcal{O}_K/P$ is a field which is a finite degree extension of $\mathbb{Z}_p/p\mathbb{Z}_p = \mathbb{F}_p$. The residue field degree is the degree of this extension: $f = [\mathcal{O}_K/P : \mathbb{F}_p]$.

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- Last edited by John Cremona on 2018-05-23 15:02:11

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- 2018-05-23 15:02:11 by John Cremona (Reviewed)