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Let $K$ be a finite extension of $\Q_p$, and $K^{un}$ its unramified subfield. Then the unramified degree of $K$ is the degree $[K^{un}:\Q_p]$.

Since $\Q_p$ has a unique unramified extension of degree $n$ for each positive integer $n$, the unramified degree of an extension determines its unramified subfield.

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  • Last edited by John Jones on 2018-07-04 23:31:23
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