List questions from p-adic-number-theory

Published on 15 May 2015 - 10:40

522

Views

A extending the p-adic valuation to a quadratic extension of $\mathbb{Q}_p$

Published on 27 Mar 2026 - 2:07

976

Views

Squares in $\mathbb Q_p$ are $p^{2n}\alpha$

Published on 16 May 2015 - 14:13

76

Views

Solution of $8x^2+x+1=0\in \mathbb{Q}_2$.

Published on 16 May 2015 - 15:40

62

Views

Showing $\mathbf Z_2/8\mathbf Z_2\simeq\mathbf Z/8\mathbf Z$

Published on 16 May 2015 - 20:14

267

Views

Roots of $X^2-z$ in $2$-adics

Published on 18 May 2015 - 8:35

1.6k

Views

Hensel's lemma & $p$-adic polynomial roots

Published on 25 Mar 2026 - 6:10

80

Views

Show that $U_i \rightarrow U_{i+e}, x \mapsto x^p$ is an isomorphism

Published on 23 May 2015 - 15:45

43

Views

Why is $m \infty$ the conductor of $K = \mathbb{Q}(\zeta_m)/\mathbb{Q}$?

Published on 27 Mar 2026 - 22:04

1k

Views

In $\mathbb Q_p$, proving every open ball is the disjoint union of more than one open ball

Published on 23 May 2015 - 20:53

581

Views

Which properties determine the uniqueness of the local Artin map?

Published on 26 Mar 2026 - 14:20

603

Views

The group $(1+p\mathbb Z_p)/(1+p^{n}\mathbb Z_p)$

Published on 24 May 2015 - 13:40

523

Views

Structure of the group $\{1+p\mathbb Z_p \}$

Published on 24 May 2015 - 22:21

595

Views

Fermat's little theorem for p-adic integers

Published on 29 Mar 2026 - 20:43

482

Views

Roadmap to $p$-adic numbers: where a self-learner should look for references

Published on 25 May 2015 - 21:12

List Question

Questions about p-adic numbers

A extending the p-adic valuation to a quadratic extension of $\mathbb{Q}_p$

Squares in $\mathbb Q_p$ are $p^{2n}\alpha$

Solution of $8x^2+x+1=0\in \mathbb{Q}_2$.

Showing $\mathbf Z_2/8\mathbf Z_2\simeq\mathbf Z/8\mathbf Z$

Roots of $X^2-z$ in $2$-adics

Hensel's lemma & $p$-adic polynomial roots

Show that $U_i \rightarrow U_{i+e}, x \mapsto x^p$ is an isomorphism

Why is $m \infty$ the conductor of $K = \mathbb{Q}(\zeta_m)/\mathbb{Q}$?

In $\mathbb Q_p$, proving every open ball is the disjoint union of more than one open ball

Which properties determine the uniqueness of the local Artin map?

The group $(1+p\mathbb Z_p)/(1+p^{n}\mathbb Z_p)$

Structure of the group $\{1+p\mathbb Z_p \}$

Fermat's little theorem for p-adic integers

Roadmap to $p$-adic numbers: where a self-learner should look for references

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