Question

Let $K$ and $K'$ be local field, and $v$ and $v'$ be it's valuation. Suppose $K'/K$ is unramified

score 36 · Answer 1 · 2021-09-17 18:08:55

36

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Let $K$ and $K'$ be local field, and $v$ and $v'$ be it's valuation. Suppose $K'/K$ is unramified

Published on 17 Sep 2021 - 18:08

score 224 · Answer 2 · 2026-03-25 09:50:15

224

Views

Example of degree $n$ ramified, but not totally ramified extension

Published on 25 Mar 2026 - 9:50

score 77 · Answer 3 · 2021-10-03 20:21:50

77

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Question about p.165 in Local Fields by Cassels

Published on 03 Oct 2021 - 20:21

score 59 · Answer 4 · 2021-10-05 04:25:45

59

Views

$j∈R$ and $256(1-λ(1-λ))^3-j λ^2(1-λ)^2＝0$ implies $λ∈R$ and $λ$ is not congruent to $0$ or $1$ mod $M$

Published on 05 Oct 2021 - 4:25

score 99 · Answer 5 · 2021-10-05 20:10:42

99

Views

Ring of integers of $\mathbb{Q}_p(α) $

Published on 05 Oct 2021 - 20:10

score 64 · Answer 6 · 2021-10-06 07:35:08

64

Views

type of reduction does not change under unramified extension

Published on 06 Oct 2021 - 7:35

score 129 · Answer 7 · 2021-10-06 12:39:11

129

Views

Inertia group $I_K$ is isomorphic to $\operatorname{Gal}(\bar K /K^{nr})$ as a group

Published on 06 Oct 2021 - 12:39

score 331 · Answer 8 · 2026-03-26 13:45:20

331

Views

Definition of discriminant of local field

Published on 26 Mar 2026 - 13:45

score 42 · Answer 9 · 2026-03-25 09:50:20

42

Views

Let $K$ be a local field and $K'$ be it's finite extension. Then, why ${K'}^{nr}/K^{nr}$ is finite extension?

Published on 25 Mar 2026 - 9:50

score 110 · Answer 10 · 2026-03-25 14:22:53

110

Views

Using Hensel lemma to find roots in valuation rings

Published on 25 Mar 2026 - 14:22

score 176 · Answer 11 · 2021-11-27 23:49:13

176

Views

Are rings of power series over a local field complete?

Published on 27 Nov 2021 - 23:49

score 288 · Answer 12 · 2021-11-29 04:53:27

288

Views

Calculating the ramification and inertia degree of $\mathbb{Q}_2(\sqrt{3}, \sqrt{7})$ and $\mathbb{Q}_2(\sqrt{3}, \sqrt{2})$ over $\mathbb{Q}_2$

Published on 29 Nov 2021 - 4:53

score 82 · Answer 13 · 2021-12-02 21:23:46

82

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An infinite family of Artin-Schreier polynomials which all split in $\mathbf{F}_q(\!(\theta)\!)$

Published on 02 Dec 2021 - 21:23

score 176 · Answer 14 · 2021-12-05 19:26:55

176

Views

Definition of $\mathfrak{p}$-adic field in Cassels

Published on 05 Dec 2021 - 19:26

score 98 · Answer 15 · 2021-12-06 16:54:25

98

Views

Convergence of a sequence in a non-Archimdean valuation for a field.

Published on 06 Dec 2021 - 16:54

List Question

Let $K$ and $K'$ be local field, and $v$ and $v'$ be it's valuation. Suppose $K'/K$ is unramified

Example of degree $n$ ramified, but not totally ramified extension

Question about p.165 in Local Fields by Cassels

$j∈R$ and $256(1-λ(1-λ))^3-j λ^2(1-λ)^2＝0$ implies $λ∈R$ and $λ$ is not congruent to $0$ or $1$ mod $M$

Ring of integers of $\mathbb{Q}_p(α) $

type of reduction does not change under unramified extension

Inertia group $I_K$ is isomorphic to $\operatorname{Gal}(\bar K /K^{nr})$ as a group

Definition of discriminant of local field

Let $K$ be a local field and $K'$ be it's finite extension. Then, why ${K'}^{nr}/K^{nr}$ is finite extension?

Using Hensel lemma to find roots in valuation rings

Are rings of power series over a local field complete?

Calculating the ramification and inertia degree of $\mathbb{Q}_2(\sqrt{3}, \sqrt{7})$ and $\mathbb{Q}_2(\sqrt{3}, \sqrt{2})$ over $\mathbb{Q}_2$

An infinite family of Artin-Schreier polynomials which all split in $\mathbf{F}_q(\!(\theta)\!)$

Definition of $\mathfrak{p}$-adic field in Cassels

Convergence of a sequence in a non-Archimdean valuation for a field.

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