Question

For a nonarchimedean field $K$, does the group of units of $\mathcal{O}_K$ being compact imply that $K$ is local?

score 65 · Answer 1 · 2023-03-01 22:37:39

65

Views

For a nonarchimedean field $K$, does the group of units of $\mathcal{O}_K$ being compact imply that $K$ is local?

Published on 01 Mar 2023 - 22:37

score 39 · Answer 2 · 2023-03-16 11:03:03

39

Views

Possible failure of $ef=n$ for a degree $n$ extension of a field complete to a nondiscrete nonarchimedean valuation?

Published on 16 Mar 2023 - 11:03

score 247 · Answer 3 · 2023-03-16 18:00:59

247

Views

Why do we assume that the residue field extension is separable in the definition of unramified

Published on 16 Mar 2023 - 18:00

score 72 · Answer 4 · 2023-03-17 07:34:07

72

Views

Frobenius map of Witt vectors

Published on 17 Mar 2023 - 7:34

score 138 · Answer 5 · 2023-03-21 10:27:16

138

Views

Norm of a root of unity $\zeta$ is $1$ only if $\zeta=1$?

Published on 21 Mar 2023 - 10:27

score 86 · Answer 6 · 2023-03-27 02:24:07

86

Views

Elements of a local field with trace in $\mathbb Z_p$

Published on 27 Mar 2023 - 2:24

score 100 · Answer 7 · 2023-03-30 20:42:36

100

Views

JS Milne Algebraic Number Theory 8.6 : normalized absolute values for local fields

Published on 30 Mar 2023 - 20:42

score 21 · Answer 8 · 2023-03-31 07:29:42

21

Views

Finding $\dfrac{\sigma(u)}{u}=\alpha$ for local field $K$, $L$ unramified over $K$, $\sigma$ being Frobenius of $L/K$ and $\alpha$ having norm 1.

Published on 31 Mar 2023 - 7:29

score 57 · Answer 9 · 2023-03-31 08:09:11

57

Views

A uniformizer of a finite extension of $\mathbb{Q}_p$

Published on 31 Mar 2023 - 8:09

score 45 · Answer 10 · 2023-04-16 05:42:38

45

Views

Example of rational jumps in upper ramification filtration

Published on 16 Apr 2023 - 5:42

score 89 · Answer 11 · 2023-04-17 10:56:42

89

Views

Why Chebotarev's density theorem implies $ \exists {v \in Ω_L}$ such that $Gal(L_v/K_{v'})$ is generated by $\sigma^2$?

Published on 17 Apr 2023 - 10:56

score 72 · Answer 12 · 2023-04-17 19:37:30

72

Views

When is a norm of a formal power series over a local field a polynomial?

Published on 17 Apr 2023 - 19:37

score 117 · Answer 13 · 2023-04-19 16:00:50

117

Views

Surjectivity of norm map on principal units in a totally ramified extension of local fields

Published on 19 Apr 2023 - 16:00

score 46 · Answer 14 · 2023-04-19 23:47:04

46

Views

If there exists a prime $l$ such that $l$ spilts in $K$, why does that imply there exists a place of $K$, which satisfies $K_v \cong \Bbb{Q}_l$?

Published on 19 Apr 2023 - 23:47

score 111 · Answer 15 · 2023-04-24 10:52:16

111

Views

Step in Yoshida's proof of Hasse-Arf theorem

Published on 24 Apr 2023 - 10:52

List Question

For a nonarchimedean field $K$, does the group of units of $\mathcal{O}_K$ being compact imply that $K$ is local?

Possible failure of $ef=n$ for a degree $n$ extension of a field complete to a nondiscrete nonarchimedean valuation?

Why do we assume that the residue field extension is separable in the definition of unramified

Frobenius map of Witt vectors

Norm of a root of unity $\zeta$ is $1$ only if $\zeta=1$?

Elements of a local field with trace in $\mathbb Z_p$

JS Milne Algebraic Number Theory 8.6 : normalized absolute values for local fields

Finding $\dfrac{\sigma(u)}{u}=\alpha$ for local field $K$, $L$ unramified over $K$, $\sigma$ being Frobenius of $L/K$ and $\alpha$ having norm 1.

A uniformizer of a finite extension of $\mathbb{Q}_p$

Example of rational jumps in upper ramification filtration

Why Chebotarev's density theorem implies $ \exists {v \in Ω_L}$ such that $Gal(L_v/K_{v'})$ is generated by $\sigma^2$?

When is a norm of a formal power series over a local field a polynomial?

Surjectivity of norm map on principal units in a totally ramified extension of local fields

If there exists a prime $l$ such that $l$ spilts in $K$, why does that imply there exists a place of $K$, which satisfies $K_v \cong \Bbb{Q}_l$?

Step in Yoshida's proof of Hasse-Arf theorem

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