List questions from p-adic-number-theory

Published on 29 Mar 2026 - 16:24

118

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What would be the image of $1+\pi O_K$ under the field norm?

Published on 29 Sep 2021 - 14:05

145

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Why algebraic closure of $\Bbb F_p$ is gained by adjoining primitive $n$-th ($n$ is coprime to $p$) root of unity to $\Bbb F_p$?

Published on 29 Sep 2021 - 16:34

352

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Verify: $a,b$ be positive rational numbers such that for infinitely many integers $n,$ $a^n-b^n$ is an integer, Prove that $a,b$ are also integers.

Published on 10 Oct 2021 - 2:38

71

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any $x$ which is algebraic of degree $n$ over $\mathbb Q_2$ has a unique series expansion $ x = \sum 2^{u_j} $

Published on 11 Oct 2021 - 14:21

256

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Incompleteness of algebraic closure of p-adic number field, from $9$ years ago question

Published on 11 Oct 2021 - 20:16

390

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How to apply the Krasner's lemma to prove $\mathbb C_p$ is algebraically closed?

Published on 12 Oct 2021 - 18:11

90

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Matrix congruences

Published on 01 Apr 2026 - 2:09

550

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Most intuitive diagram of p-adic distances?

Published on 15 Oct 2021 - 0:00

64

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Working with subset of complex numbers 'p-adically'?

Published on 16 Oct 2021 - 22:04

297

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Combined real + p-adic numbers?

Published on 18 Oct 2021 - 17:06

85

Views

Integral basis for totally ramified extensions of $p$-adic fields

Published on 26 Mar 2026 - 22:13

175

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Extensions of the $p$-adic valuation to $\overline{\mathbb{Q}}$

Published on 29 Mar 2026 - 2:17

108

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Silverman AEC: Lemma IV.6.3 [on the convergence of formal logarithm]

Published on 25 Mar 2026 - 6:04

186

Views

Tensor product with $\mathbf{Q}_p/\mathbf{Z}_p$

Published on 05 Nov 2021 - 19:42

List Question

Example of $E_0(K)$ which satisfies $[E(K):E_0(K)]＝2$

What would be the image of $1+\pi O_K$ under the field norm?

Why algebraic closure of $\Bbb F_p$ is gained by adjoining primitive $n$-th ($n$ is coprime to $p$) root of unity to $\Bbb F_p$?

Verify: $a,b$ be positive rational numbers such that for infinitely many integers $n,$ $a^n-b^n$ is an integer, Prove that $a,b$ are also integers.

any $x$ which is algebraic of degree $n$ over $\mathbb Q_2$ has a unique series expansion $ x = \sum 2^{u_j} $

Incompleteness of algebraic closure of p-adic number field, from $9$ years ago question

How to apply the Krasner's lemma to prove $\mathbb C_p$ is algebraically closed?

Matrix congruences

Most intuitive diagram of p-adic distances?

Working with subset of complex numbers 'p-adically'?

Combined real + p-adic numbers?

Integral basis for totally ramified extensions of $p$-adic fields

Extensions of the $p$-adic valuation to $\overline{\mathbb{Q}}$

Silverman AEC: Lemma IV.6.3 [on the convergence of formal logarithm]

Tensor product with $\mathbf{Q}_p/\mathbf{Z}_p$

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