List questions from class-field-theory

Published on 25 Mar 2026 - 20:59

55

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Are $(K_v)^{ab}$ and $(K^{ab})_v$ the same thing?

Published on 18 Nov 2021 - 20:02

373

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On the maximal abelian pro-$p$ extension unramified outside $p$ and the Leopoldt's conjecture

Published on 10 Dec 2021 - 15:39

160

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For each number field $K$ with place $\mathfrak{p}$, prove that $K_{\mathfrak{p}}^{\mathrm{ab}} = K_{\mathfrak{p}} K^{\mathrm{ab}}$

Published on 11 Dec 2021 - 9:18

57

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Subgroups of Weil-Deligne group

Published on 11 Dec 2021 - 23:43

113

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What is the Galois group of narrow Hilbert class field over Hilbert class field?

Published on 20 Dec 2021 - 17:24

95

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What is the Weber class polynomial?

Published on 28 Dec 2021 - 20:45

113

Views

Maximal abelian $p$-extension unramified away from $p$

Published on 26 Mar 2026 - 12:35

61

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Proposition 10.4 in Neukirch's Algebraic Number Theory

Published on 25 Mar 2026 - 23:53

113

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Compatibility and consistency between two definitions of cohomology in two books (about coboundary operators and 1-cocycles and computing cohomology)

Published on 08 Jan 2022 - 20:24

148

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Explicit Local Fundamental Class

Published on 27 Mar 2026 - 7:47

60

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A very simple problem on 1-cocycles

Published on 10 Jan 2022 - 20:31

66

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Another question on 1-cocycles (explicite computation of 1-cocycles)

Published on 12 Jan 2022 - 19:31

31

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Obstruction of existing a 2-cocycle in Galois cohomology with given local components

Published on 27 Mar 2026 - 17:24

113

Views

Let $V$ be p-torsion representation. Then, $H^n(K,V)＝0$ for all $n≧3$ in the context of class field theory

Published on 07 Feb 2022 - 12:52

List Question

$2^n$-th rational reciprocity laws

Are $(K_v)^{ab}$ and $(K^{ab})_v$ the same thing?

On the maximal abelian pro-$p$ extension unramified outside $p$ and the Leopoldt's conjecture

For each number field $K$ with place $\mathfrak{p}$, prove that $K_{\mathfrak{p}}^{\mathrm{ab}} = K_{\mathfrak{p}} K^{\mathrm{ab}}$

Subgroups of Weil-Deligne group

What is the Galois group of narrow Hilbert class field over Hilbert class field?

What is the Weber class polynomial?

Maximal abelian $p$-extension unramified away from $p$

Proposition 10.4 in Neukirch's Algebraic Number Theory

Compatibility and consistency between two definitions of cohomology in two books (about coboundary operators and 1-cocycles and computing cohomology)

Explicit Local Fundamental Class

A very simple problem on 1-cocycles

Another question on 1-cocycles (explicite computation of 1-cocycles)

Obstruction of existing a 2-cocycle in Galois cohomology with given local components

Let $V$ be p-torsion representation. Then, $H^n(K,V)＝0$ for all $n≧3$ in the context of class field theory

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