List questions from unramified-extension

Published on 03 Apr 2026 - 3:35

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Ramification of primes on $\overline{\mathbb Q}$

Published on 29 Apr 2026 - 12:54

58

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Is the unramified local Langlands conjecture true?

Published on 29 Apr 2026 - 12:54

18

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proof of existence of totally ramified extension

Published on 29 Apr 2026 - 12:54

16

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abelian extension of local field is unramified

Published on 29 Apr 2026 - 12:28

64

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Tamely extension of the maximal unramified extension of a local field

Published on 29 Apr 2026 - 12:54

95

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étale, smooth, and unramified for product of schemes

Published on 29 Apr 2026 - 12:54

81

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$K_v(a^{1/m}) /K_v$ is unramified if only if $v(a)\equiv0 \pmod m$

Published on 29 Apr 2026 - 12:54

231

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Example of degree $n$ ramified, but not totally ramified extension

Published on 29 Apr 2026 - 12:54

44

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Let $K$ be a local field and $K'$ be it's finite extension. Then, why ${K'}^{nr}/K^{nr}$ is finite extension?

Published on 29 Apr 2026 - 12:54

172

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Ramification index example.

Published on 29 Apr 2026 - 12:54

53

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Decomposition of unramified primes in normal closure of pure quintic field

Published on 29 Apr 2026 - 12:54

62

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Let $\Bbb{Q}_p⊆L_0⊆L$, where $L$ is extension of $\Bbb{Q}_p$ and $L_0$ be maximal unramified sub extension of $L/\Bbb{Q}_p$.

Published on 29 Apr 2026 - 12:54

105

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Residue class field of $\mathbb{Q}_p(\zeta_m)$, where $(m,p) = 1$, is $\mathbb{F}_p(\zeta_m)$

Published on 29 Apr 2026 - 12:54

134

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Unramified extensions of local fields

Published on 29 Apr 2026 - 12:54

List Question

Unramified extension in CDVF

Ramification of primes on $\overline{\mathbb Q}$

Is the unramified local Langlands conjecture true?

proof of existence of totally ramified extension

abelian extension of local field is unramified

Tamely extension of the maximal unramified extension of a local field

étale, smooth, and unramified for product of schemes

$K_v(a^{1/m}) /K_v$ is unramified if only if $v(a)\equiv0 \pmod m$

Example of degree $n$ ramified, but not totally ramified extension

Let $K$ be a local field and $K'$ be it's finite extension. Then, why ${K'}^{nr}/K^{nr}$ is finite extension?

Ramification index example.

Decomposition of unramified primes in normal closure of pure quintic field

Let $\Bbb{Q}_p⊆L_0⊆L$, where $L$ is extension of $\Bbb{Q}_p$ and $L_0$ be maximal unramified sub extension of $L/\Bbb{Q}_p$.

Residue class field of $\mathbb{Q}_p(\zeta_m)$, where $(m,p) = 1$, is $\mathbb{F}_p(\zeta_m)$

Unramified extensions of local fields

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