List questions from p-adic-number-theory

312

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The number of solutions of the equation $x^n+y^n=1$ over $\mathbb{Z}_p$ with $\mathbb{Z}_p=\{\alpha\in \mathbb{Q}_p:|\alpha|_p\le 1\}$.

Published on 28 Mar 2026 - 3:33

1.9k

Views

Newton polygons

Published on 22 Apr 2012 - 19:19

688

Views

The polynomial $x^p-x-1/p$ over $\mathbb Q_p$

Published on 23 Apr 2012 - 5:48

990

Views

P-adic integers

Published on 25 Apr 2012 - 11:22

858

Views

What are the branches of the $p$-adic zeta function?

Published on 25 Mar 2026 - 22:25

636

Views

Why is $O_K\otimes \mathbb{Z}_p\cong \oplus_{\mathfrak{p}|p}O_{K,\mathfrak{p}}$?

Published on 28 Apr 2012 - 2:43

1.4k

Views

Divergent series and $p$-adics

Published on 06 May 2012 - 22:57

261

Views

Line in a proof on p69 in Cassel's Local Fields

Published on 07 May 2012 - 9:46

130

Views

Choosing an isomorphism $\tau:\overline{\mathbf{Q}}_p\simeq\mathbf{C}$; how do things depend on choice of $\tau$?

Published on 08 Jun 2012 - 22:25

2k

Views

Unramified p-adic extension implies Galois

Published on 10 Jun 2012 - 14:22

2.9k

Views

The $p$-adic integers as a profinite group

Published on 11 Jun 2012 - 1:11

165

Views

Liftings in unramified extensions of $\Bbb Z_p$

Published on 13 Jun 2012 - 16:09

204

Views

Lifting additive characters

Published on 26 Mar 2026 - 3:09

1k

Views

Why does the equation $x^2-82y^2=\pm2$ have solutions in every $\mathbb{Z}_p$ but not in $\mathbb{Z}$?

Published on 28 Mar 2026 - 7:00

316

Views

diagonalizing a matrix over the $\ell$-adics

Published on 05 Jul 2012 - 17:48

List Question

The number of solutions of the equation $x^n+y^n=1$ over $\mathbb{Z}_p$ with $\mathbb{Z}_p=\{\alpha\in \mathbb{Q}_p:|\alpha|_p\le 1\}$.

Newton polygons

The polynomial $x^p-x-1/p$ over $\mathbb Q_p$

P-adic integers

What are the branches of the $p$-adic zeta function?

Why is $O_K\otimes \mathbb{Z}_p\cong \oplus_{\mathfrak{p}|p}O_{K,\mathfrak{p}}$?

Divergent series and $p$-adics

Line in a proof on p69 in Cassel's Local Fields

Choosing an isomorphism $\tau:\overline{\mathbf{Q}}_p\simeq\mathbf{C}$; how do things depend on choice of $\tau$?

Unramified p-adic extension implies Galois

The $p$-adic integers as a profinite group

Liftings in unramified extensions of $\Bbb Z_p$

Lifting additive characters

Why does the equation $x^2-82y^2=\pm2$ have solutions in every $\mathbb{Z}_p$ but not in $\mathbb{Z}$?

diagonalizing a matrix over the $\ell$-adics

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