List questions from local-field

Published on 20 Mar 2026 - 15:55

76

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Given a local field is the maximal unramifield extension always finite?

Published on 21 Mar 2026 - 21:45

128

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$(K^)$ in $K^$

Published on 17 Mar 2026 - 12:15

56

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How do we know that reducing $E/K$ commutes with the addition law for $K$ local field

Published on 19 Mar 2026 - 22:19

230

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How is $\operatorname{Gal}(K^{nr}/K)$ isomorphic to $\operatorname{Gal}(\bar{k}/k)$?

Published on 20 Mar 2026 - 7:00

874

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Extending a valuation of a local field

Published on 20 Mar 2026 - 5:34

567

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On the Galois group of the maximal $p$-abelian $p$-ramified extension of a number field

Published on 17 Mar 2026 - 15:55

235

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Finite extension of $K$,a finite extension of $\mathbb{Q}_p$, that is Galois?

Published on 20 Mar 2026 - 9:29

68

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Why is $E[2]$ of $E: y^2 = x^3 - p$ over $\mathbb{Q}_p$ ramified?

Published on 22 Mar 2026 - 11:31

333

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Are there any $\mathbb{Q}_p$ which contains the third root of unity?

Published on 22 Mar 2026 - 5:36

150

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Given a local field $K$ how does one obtain the maximal unramified extension of $K$?

Published on 19 Mar 2026 - 23:42

46

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Is $\mathbb{Q}_p(p^{2/3})$ an unramified extension?

Published on 24 Mar 2026 - 0:52

307

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Question about why inertia subgroup is a closed subgroup of the Galois group

Published on 22 Mar 2026 - 20:37

54

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How can I prove that $\bigcap\limits_{n=0}^{+\infty} \Gamma_{j,n}=\emptyset$?

Published on 17 Mar 2026 - 6:01

889

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Dedekind domain with finite prime ideals is PID (a corollary on Serre's "Local fields" book).

Published on 24 Mar 2026 - 15:19

List Question

What is meant by a category of unramified extension of $K$ (a local field)?

Given a local field is the maximal unramifield extension always finite?

$(K^)$ in $K^$

How do we know that reducing $E/K$ commutes with the addition law for $K$ local field

How is $\operatorname{Gal}(K^{nr}/K)$ isomorphic to $\operatorname{Gal}(\bar{k}/k)$?

Extending a valuation of a local field

On the Galois group of the maximal $p$-abelian $p$-ramified extension of a number field

Finite extension of $K$,a finite extension of $\mathbb{Q}_p$, that is Galois?

Why is $E[2]$ of $E: y^2 = x^3 - p$ over $\mathbb{Q}_p$ ramified?

Are there any $\mathbb{Q}_p$ which contains the third root of unity?

Given a local field $K$ how does one obtain the maximal unramified extension of $K$?

Is $\mathbb{Q}_p(p^{2/3})$ an unramified extension?

Question about why inertia subgroup is a closed subgroup of the Galois group

How can I prove that $\bigcap\limits_{n=0}^{+\infty} \Gamma_{j,n}=\emptyset$?

Dedekind domain with finite prime ideals is PID (a corollary on Serre's "Local fields" book).

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