Question

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

score 117 · Answer 1 · 2023-04-19 16:00:50

117

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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 2 · 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 69 · Answer 3 · 2023-04-20 16:48:07

69

Views

About (wild) ramification of an abelian extension and its conductor

Published on 20 Apr 2023 - 16:48

score 111 · Answer 4 · 2023-04-24 10:52:16

111

Views

Step in Yoshida's proof of Hasse-Arf theorem

Published on 24 Apr 2023 - 10:52

score 85 · Answer 5 · 2026-03-25 09:13:56

85

Views

Ramification Index 2 in Galois closure of field with squarefree discriminant

Published on 25 Mar 2026 - 9:13

score 78 · Answer 6 · 2023-06-18 14:55:44

78

Views

Galois extension of $\mathbb{Q}_p$ with Galois group $\mathbb{Z}/2\mathbb{Z}$

Published on 18 Jun 2023 - 14:55

score 99 · Answer 7 · 2023-07-01 13:08:01

99

Views

Is the splitting field of $x^3+2x^2-x-3$ a totally ramified extension of $\mathbb Q_5$?

Published on 01 Jul 2023 - 13:08

score 146 · Answer 8 · 2023-07-16 11:25:44

146

Views

Infinite primes in number fields

Published on 16 Jul 2023 - 11:25

score 93 · Answer 9 · 2023-07-29 00:03:48

93

Views

Example of unramified covering map of degree d

Published on 29 Jul 2023 - 0:03

score 23 · Answer 10 · 2026-03-25 06:34:57

23

Views

How to find vanishing order of coefficients of Newton polynomial?

Published on 25 Mar 2026 - 6:34

score 45 · Answer 11 · 2026-03-26 01:10:30

45

Views

Prime of order is regular iff its decomposition in the normalization is trivial.

Published on 26 Mar 2026 - 1:10

score 21 · Answer 12 · 2023-10-10 09:48:57

21

Views

What is the ramification group of a curve at a point

Published on 10 Oct 2023 - 9:48

score 147 · Answer 13 · 2023-10-26 05:15:18

Why $ev_p$ is normalized, where $v_p$ is the $p$-adic valuation of $\mathbb{Q}_p$ being extended to $K$? ( Neukirch's ANT book, (5.5) Proposition)

score 15 · Answer 14 · 2023-11-16 05:41:19

15

Views

Ramification theory, What is the relation between $K_S$ and $L_S$?

Published on 16 Nov 2023 - 5:41

score 163 · Answer 15 · 2023-11-21 00:00:15

163

Views

Does there exists a quadratic extension $L$ of $K$, in which $p_1,p_2,\ldots,p_n$ ramifies in $L/K$?

Published on 21 Nov 2023 - 0:00

List Question

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 $K_v \cong \Bbb{Q}_l$?

About (wild) ramification of an abelian extension and its conductor

Step in Yoshida's proof of Hasse-Arf theorem

Ramification Index 2 in Galois closure of field with squarefree discriminant

Galois extension of $\mathbb{Q}_p$ with Galois group $\mathbb{Z}/2\mathbb{Z}$

Is the splitting field of $x^3+2x^2-x-3$ a totally ramified extension of $\mathbb Q_5$?

Infinite primes in number fields

Example of unramified covering map of degree d

How to find vanishing order of coefficients of Newton polynomial?

Prime of order is regular iff its decomposition in the normalization is trivial.

What is the ramification group of a curve at a point

Why $ev_p$ is normalized, where $v_p$ is the $p$-adic valuation of $\mathbb{Q}_p$ being extended to $K$? ( Neukirch's ANT book, (5.5) Proposition)

Ramification theory, What is the relation between $K_S$ and $L_S$?

Does there exists a quadratic extension $L$ of $K$, in which $p_1,p_2,\ldots,p_n$ ramifies in $L/K$?

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