Question

Understanding some square root notation in LMFDB occuring in the definition of a p-adic field

score 92 · Answer 1 · 2020-11-24 14:36:31

92

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Understanding some square root notation in LMFDB occuring in the definition of a p-adic field

Published on 24 Nov 2020 - 14:36

score 165 · Answer 2 · 2020-11-24 15:16:55

165

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Why is $x^4-3x^2+18$ irreducible over the $3$-adics?

Published on 24 Nov 2020 - 15:16

score 178 · Answer 3 · 2020-11-24 18:55:26

178

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How to explicitly describe the generator of the Galois group of the extension defined by $x^4-3x^2+18$?

Published on 24 Nov 2020 - 18:55

score 75 · Answer 4 · 2026-03-27 00:58:10

75

Views

Galois action on $K\otimes_{\mathbb{Q}} \mathbb{Q}_\ell$

Published on 27 Mar 2026 - 0:58

score 133 · Answer 5 · 2026-03-27 06:07:48

133

Views

Compactness of units in ring of integers

Published on 27 Mar 2026 - 6:07

score 37 · Answer 6 · 2020-11-30 18:38:02

37

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I want to show that $\ker(h)=2\Bbb Z_2^2=2(\Bbb Z_2 \times\Bbb Z_2)$

Published on 30 Nov 2020 - 18:38

score 127 · Answer 7 · 2026-03-26 19:02:46

127

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Galois group of the compositum of a non-totally-ramified and a the unramified extension of $\mathbb{Q}_p$ of prime power degree

Published on 26 Mar 2026 - 19:02

score 427 · Answer 8 · 2020-12-03 12:23:36

427

Views

Is the Gauss norm for $p$-adic power series a supremum of values taken over the unit disk?

Published on 03 Dec 2020 - 12:23

score 99 · Answer 9 · 2026-03-25 09:37:15

99

Views

Is $\frac{10}{459}$ a cube in $\Bbb{Q}_3$?

Published on 25 Mar 2026 - 9:37

score 64 · Answer 10 · 2020-12-04 17:02:28

64

Views

Computing the reduction of a quotient of a quartic polynomial defining an extension over $\mathbb{Q}_3$

Published on 04 Dec 2020 - 17:02

score 43 · Answer 11 · 2020-12-05 09:18:39

43

Views

To show all the coefficients $c_i, \ 1 \leq i \leq n-1$ lie in the maximal ideal $p \mathbb{Z}_p$

Published on 05 Dec 2020 - 9:18

score 389 · Answer 12 · 2026-03-28 14:00:31

389

Views

Let $R$ and $R'$ be two discrete valuation rings of $K$. Is $R=R'$?

Published on 28 Mar 2026 - 14:00

score 645 · Answer 13 · 2020-12-13 07:41:21

645

Views

Can we have $n$-adic integers?

Published on 13 Dec 2020 - 7:41

score 76 · Answer 14 · 2020-12-13 17:38:25

76

Views

Constructing elements of $\mathbb{Z}_p[\Gamma_n]$ from $\mathbb{Z}_p[\operatorname{Gal}(\mathbb{Q}(\zeta_{p^{n+1}})/\mathbb{Q})]$

Published on 13 Dec 2020 - 17:38

score 640 · Answer 15 · 2020-12-15 10:52:10

640

Views

the ways completion of p-adic integers

Published on 15 Dec 2020 - 10:52

List Question

Understanding some square root notation in LMFDB occuring in the definition of a p-adic field

Why is $x^4-3x^2+18$ irreducible over the $3$-adics?

How to explicitly describe the generator of the Galois group of the extension defined by $x^4-3x^2+18$?

Galois action on $K\otimes_{\mathbb{Q}} \mathbb{Q}_\ell$

Compactness of units in ring of integers

I want to show that $\ker(h)=2\Bbb Z_2^2=2(\Bbb Z_2 \times\Bbb Z_2)$

Galois group of the compositum of a non-totally-ramified and a the unramified extension of $\mathbb{Q}_p$ of prime power degree

Is the Gauss norm for $p$-adic power series a supremum of values taken over the unit disk?

Is $\frac{10}{459}$ a cube in $\Bbb{Q}_3$?

Computing the reduction of a quotient of a quartic polynomial defining an extension over $\mathbb{Q}_3$

To show all the coefficients $c_i, \ 1 \leq i \leq n-1$ lie in the maximal ideal $p \mathbb{Z}_p$

Let $R$ and $R'$ be two discrete valuation rings of $K$. Is $R=R'$?

Can we have $n$-adic integers?

Constructing elements of $\mathbb{Z}_p[\Gamma_n]$ from $\mathbb{Z}_p[\operatorname{Gal}(\mathbb{Q}(\zeta_{p^{n+1}})/\mathbb{Q})]$

the ways completion of p-adic integers

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