A **local field** is a field $K$ with a non-trivial absolute value $|\ |$ that is locally compact in the topology induced by the distance metric $d(x,y):=|x-y|$.

An **archimedean local field** is a local field whose absolute value is archimedean; such a field is isomorphic to $\R$ or $\C$.

A **nonarchimedean local field** is a local field whose absolute value is nonarchimedean; such fields are isomorphic to finite extensions of $\Q_p$ when $K$ has characteristic zero, and to a finite extension of $\F_p((t))$ when $K$ characteristic $p$. In both cases $p$ is the characteristic of the residue field.

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- Review status: reviewed
- Last edited by John Jones on 2020-10-26 12:20:59

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**History:**(expand/hide all)

- 2020-10-26 12:20:59 by John Jones (Reviewed)
- 2020-10-26 12:19:38 by John Jones
- 2020-10-24 16:16:22 by Andrew Sutherland
- 2020-10-24 16:13:35 by Andrew Sutherland
- 2020-10-24 15:42:22 by Andrew Sutherland
- 2020-10-24 15:39:50 by Andrew Sutherland
- 2020-10-24 15:38:37 by Andrew Sutherland

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