List questions from local-field

Published on 14 Sep 2022 - 14:15

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Is $\mathbb{Z}_p$ the only discrete valuation ring of $\mathbb{Q}_p$

Published on 28 Sep 2022 - 23:36

61

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Reduction of an abelian variety modulo powers of a prime

Published on 25 Mar 2026 - 16:03

143

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Compositum of infinitely many unramified extensions is unramified

Published on 27 Mar 2026 - 0:05

74

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$K\subset L$ is finite implies $\mathcal O_K/ \mathfrak{m}_K \subset \mathcal O_L/\mathfrak{m}_L$ is finite

Published on 13 Oct 2022 - 23:09

37

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Reference for proving $[L:K]=e[\mathcal O_L/\mathfrak{m}_L:\mathcal O_K/ \mathfrak{m}_K]$ for e - ramification index

Published on 14 Oct 2022 - 1:10

47

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Why for discrete valuation fields $K\subset L$ it holds that $\mathcal O_K \subset \mathcal O_L$?

Published on 20 Oct 2022 - 14:57

65

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Why is $K^{\mathrm{sep}}$ dense in $K_v^{\mathrm{sep}}$?

Published on 24 Feb 2026 - 0:46

40

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Automating modular arithmetic in local fields using MAGMA

Published on 23 Feb 2026 - 4:51

73

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On the construction of the de Rham period ring

Published on 01 Nov 2022 - 1:44

46

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Element in ring of integers of $\overline{\mathbb{Q}}_p$

Published on 05 Nov 2022 - 14:52

61

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Higher ramification for cyclotomic extension of $\mathbb{Q}_p$

Published on 13 Nov 2022 - 11:57

44

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Consequences of definitions in Local fields

Published on 27 Mar 2026 - 0:10

57

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Serre's Local Fields, Corollary 2 in Chapter 1.6. (unramified extension of local fields).

Published on 25 Mar 2026 - 11:32

31

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Why the addition group of a local field is isomorphic to its character group?

Published on 07 Dec 2022 - 5:16

List Question

Intersections of completions of number fields

Is $\mathbb{Z}_p$ the only discrete valuation ring of $\mathbb{Q}_p$

Reduction of an abelian variety modulo powers of a prime

Compositum of infinitely many unramified extensions is unramified

$K\subset L$ is finite implies $\mathcal O_K/ \mathfrak{m}_K \subset \mathcal O_L/\mathfrak{m}_L$ is finite

Reference for proving $[L:K]=e[\mathcal O_L/\mathfrak{m}_L:\mathcal O_K/ \mathfrak{m}_K]$ for e - ramification index

Why for discrete valuation fields $K\subset L$ it holds that $\mathcal O_K \subset \mathcal O_L$?

Why is $K^{\mathrm{sep}}$ dense in $K_v^{\mathrm{sep}}$?

Automating modular arithmetic in local fields using MAGMA

On the construction of the de Rham period ring

Element in ring of integers of $\overline{\mathbb{Q}}_p$

Higher ramification for cyclotomic extension of $\mathbb{Q}_p$

Consequences of definitions in Local fields

Serre's Local Fields, Corollary 2 in Chapter 1.6. (unramified extension of local fields).

Why the addition group of a local field is isomorphic to its character group?

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