tame ramification of p-adic local fields

p 进局部域的温分歧

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Other names / variants: tamely ramified local extension

Translation evidence: Literature usage

Meaning in context

A finite extension $L/K$ of $p$-adic local fields is tamely ramified when $p\nmid e(L/K)$.

对 $p$ 进局部域的有限扩张 $L/K$，若 $p$ 不整除分歧指数，则称其温分歧。

Example

$\mathbb Q_3(\sqrt3)/\mathbb Q_3$ is tamely ramified, with $e=2$.

Usage and distinctions

Tame includes unramified extensions (e=1); wild ramification has p dividing e in this finite-residue-field setting.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. 张神星 — 代数数论讲义 v2.5 (2024-01-09)，合肥工业大学作者讲义Section 2.3.4, Definition 2.45, printed page 50 · Checked 2026-10-14

Translation sources

1. 张神星 — 代数数论讲义 v2.5 (2024-01-09)，合肥工业大学作者讲义定义2.45 温分歧，printed page 50 · Checked 2026-10-14

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