Question

Over which extensions of $\mathbb Q_2$ is $X^2+Y^2+Z^2$ isotropic?

score 518 · Answer 1 · 2020-12-29 02:03:43

518

Views

Over which extensions of $\mathbb Q_2$ is $X^2+Y^2+Z^2$ isotropic?

Published on 29 Dec 2020 - 2:03

score 148 · Answer 2 · 2026-03-28 14:06:33

148

Views

How to show that any nontrivial valuation on the field of rational numbers is equivalent to some p-adic valuation?

Published on 28 Mar 2026 - 14:06

score 223 · Answer 3 · 2021-01-05 20:32:04

223

Views

Proof that all extensions of $\mathbb{Q}_p$ are of the form $\mathbb{Q}_p[\sqrt[n]{a}]$

Published on 05 Jan 2021 - 20:32

score 48 · Answer 4 · 2021-01-07 12:26:20

48

Views

Prove: If $a \in \mathbb{Q}^*$ has a square root in $\mathbb{Q}_p$ for all primes $p$, then it has a square root in $\mathbb{Q}$

Published on 07 Jan 2021 - 12:26

score 90 · Answer 5 · 2021-01-08 18:06:53

90

Views

Determine a generator of a subextension in a non-Kummer-setting

Published on 08 Jan 2021 - 18:06

score 221 · Answer 6 · 2021-01-09 01:14:44

221

Views

Ultrafilters on naturals determine p-adic numbers

Published on 09 Jan 2021 - 1:14

score 277 · Answer 7 · 2021-01-09 12:54:28

277

Views

Convergence of series in p-adic norm

Published on 09 Jan 2021 - 12:54

score 151 · Answer 8 · 2021-01-10 01:56:28

151

Views

Convergence of sequence in p-adic integers

Published on 10 Jan 2021 - 1:56

score 84 · Answer 9 · 2021-01-10 21:42:18

84

Views

Determining the corresponding local field

Published on 10 Jan 2021 - 21:42

score 125 · Answer 10 · 2026-04-02 06:37:07

125

Views

Definition of $\Lambda$-adic cusp form

Published on 02 Apr 2026 - 6:37

score 142 · Answer 11 · 2021-01-12 22:33:43

142

Views

Galois theoretic way to find which completions of a number field are isomorphic

Published on 12 Jan 2021 - 22:33

score 226 · Answer 12 · 2021-01-14 15:50:48

226

Views

what is $\mathbb{Q}_p^\times/\mathbb{Q}_p^{\times^2}$ called?

Published on 14 Jan 2021 - 15:50

score 105 · Answer 13 · 2021-01-14 16:13:22

105

Views

Understanding the derivation of the $p$-adic numbers as the completion from $\mathbb{Q}$ wrt. the prime ideal $(p)$

Published on 14 Jan 2021 - 16:13

score 230 · Answer 14 · 2021-01-14 17:55:37

230

Views

Finite extensions of $\mathbb{Q}_p$ as completions of number fields with some valuation over a prime ideal

Published on 14 Jan 2021 - 17:55

score 359 · Answer 15 · 2026-03-27 01:00:13

359

Views

Can a generator of the ring of integers of local fields can be chosen so that it is also a uniformizer at the same time?

Published on 27 Mar 2026 - 1:00

List Question

Over which extensions of $\mathbb Q_2$ is $X^2+Y^2+Z^2$ isotropic?

How to show that any nontrivial valuation on the field of rational numbers is equivalent to some p-adic valuation?

Proof that all extensions of $\mathbb{Q}_p$ are of the form $\mathbb{Q}_p[\sqrt[n]{a}]$

Prove: If $a \in \mathbb{Q}^*$ has a square root in $\mathbb{Q}_p$ for all primes $p$, then it has a square root in $\mathbb{Q}$

Determine a generator of a subextension in a non-Kummer-setting

Ultrafilters on naturals determine p-adic numbers

Convergence of series in p-adic norm

Convergence of sequence in p-adic integers

Determining the corresponding local field

Definition of $\Lambda$-adic cusp form

Galois theoretic way to find which completions of a number field are isomorphic

what is $\mathbb{Q}_p^\times/\mathbb{Q}_p^{\times^2}$ called?

Understanding the derivation of the $p$-adic numbers as the completion from $\mathbb{Q}$ wrt. the prime ideal $(p)$

Finite extensions of $\mathbb{Q}_p$ as completions of number fields with some valuation over a prime ideal

Can a generator of the ring of integers of local fields can be chosen so that it is also a uniformizer at the same time?

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