List questions from local-field

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proof of existence of totally ramified extension

Published on 25 Mar 2026 - 9:50

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Elliptic curve theory : Injection from $\widehat{E(K)}$ to $E(K_v)$

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local fields are locally profinite

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embed roots of unity from valued field into its residue field

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25

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associate a character to an abelian extension in local class field theory

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52

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If $\mathbb Q_p(\sqrt[3]{2})$ is galois over $\mathbb Q_p$ then does $\mathbb Q_p$ necessarily contain a cube root of unity?

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12

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abelian extension of local field is unramified

Published on 25 Mar 2026 - 9:50

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galois group of completions

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Why is the valuation of a separable closure equal to $\mathbb{Q}$?

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Elliptic curves - finding which primes $p$ guarantee there are $x,y\in\mathbb{Z}_p$ on the curve

Published on 23 Feb 2024 - 16:12

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Tamely extension of the maximal unramified extension of a local field

Published on 25 Mar 2026 - 11:20

19

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Serre's definition of $U_{\mathfrak{m}}$ for $\ell$-adic representations

Published on 25 Mar 2026 - 17:37

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morphism on complete filtered group

Published on 26 Feb 2024 - 19:25

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One dimensional $\ell$-adic representations of $\mathbb{Z}_p$

Published on 19 Mar 2024 - 13:16

List Question

density of $\langle \textit{Frobenius}\rangle$ in $Gal(L/K)$

proof of existence of totally ramified extension

Elliptic curve theory : Injection from $\widehat{E(K)}$ to $E(K_v)$

local fields are locally profinite

embed roots of unity from valued field into its residue field

associate a character to an abelian extension in local class field theory

If $\mathbb Q_p(\sqrt[3]{2})$ is galois over $\mathbb Q_p$ then does $\mathbb Q_p$ necessarily contain a cube root of unity?

abelian extension of local field is unramified

galois group of completions

Why is the valuation of a separable closure equal to $\mathbb{Q}$?

Elliptic curves - finding which primes $p$ guarantee there are $x,y\in\mathbb{Z}_p$ on the curve

Tamely extension of the maximal unramified extension of a local field

Serre's definition of $U_{\mathfrak{m}}$ for $\ell$-adic representations

morphism on complete filtered group

One dimensional $\ell$-adic representations of $\mathbb{Z}_p$

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