unramified extension of p-adic local fields

p 进局部域的非分歧扩张

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Other names / variants: unramified local extension

Translation evidence: Literature usage

Meaning in context

A finite extension $L/K$ of finite extensions of $\mathbb Q_p$ having ramification index $e(L/K)=1$.

$\mathbb Q_p$ 的有限扩张间的一个分歧指数为 $1$ 的有限扩张 $L/K$。

Example

$\mathbb Q_3(i)/\mathbb Q_3$ is an unramified quadratic extension.

Usage and distinctions

For general complete discretely valued fields, separability of the residue extension is also required; it is automatic for the finite residue fields used here.

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 2.3.3, definition following Proposition 2.39, printed page 49 · Checked 2026-10-15

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§2.3.3 非分歧(惯性)，printed page 49 · Checked 2026-10-15

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