List questions from ideal-class-group

Published on 25 Mar 2026 - 6:05

166

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Showing that $\mathbf{Z}$ adjoin a primitive seventh root of unity is a UFD.

Published on 25 Mar 2026 - 4:40

58

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Class group of quadratic field extension $\mathbb Q(\sqrt{-69})$ has order 8

Published on 25 Mar 2026 - 6:05

120

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Hint for an Imaginary quadratic field question

Published on 25 Mar 2026 - 6:01

128

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Find a non-trivial element in the class group of $\mathbb{Q}( \sqrt{−5})$.

Published on 25 Mar 2026 - 4:41

72

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Totally ramified principal ideal

Published on 25 Mar 2026 - 4:37

60

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Concrete example of S-ideal class group

Published on 25 Mar 2026 - 6:01

77

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An exact sequence $1 \to {O_{K,S}}^{\times}/{{O_{K,S}}^{\times}}^2 \to K(S,2) \to Cl(K,S)[2] \to 1$

Published on 25 Mar 2026 - 4:43

81

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Neukirch 'Algebraic number theory', p73, Prop 11.6. there is a surjection $Cl(O) \to Cl(O(X))$.

Published on 25 Mar 2026 - 4:42

81

Views

Ideal class groups of number fields

Published on 05 Apr 2026 - 22:00

49

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The plane in the quadric 3-fold is not a (set-theoretic) hypersurface

Published on 25 Mar 2026 - 4:41

97

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What information does the numerical norm provide (and why)?

Published on 25 Mar 2026 - 4:38

76

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Invertible lattices

Published on 10 May 2026 - 13:23

112

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Ideal class group of $\mathbb{Q}(\sqrt[3]{5})$

Published on 25 Mar 2026 - 4:39

87

Views

There exists imaginary quadratic extension which trivialized 2-part of ideal class group

Published on 25 Mar 2026 - 4:41

List Question

Is there an 'easy' way to calculate $K_0(\mathbb{Z}[C_p])$?

Showing that $\mathbf{Z}$ adjoin a primitive seventh root of unity is a UFD.

Class group of quadratic field extension $\mathbb Q(\sqrt{-69})$ has order 8

Hint for an Imaginary quadratic field question

Find a non-trivial element in the class group of $\mathbb{Q}( \sqrt{−5})$.

Totally ramified principal ideal

Concrete example of S-ideal class group

An exact sequence $1 \to {O_{K,S}}^{\times}/{{O_{K,S}}^{\times}}^2 \to K(S,2) \to Cl(K,S)[2] \to 1$

Neukirch 'Algebraic number theory', p73, Prop 11.6. there is a surjection $Cl(O) \to Cl(O(X))$.

Ideal class groups of number fields

The plane in the quadric 3-fold is not a (set-theoretic) hypersurface

What information does the numerical norm provide (and why)?

Invertible lattices

Ideal class group of $\mathbb{Q}(\sqrt[3]{5})$

There exists imaginary quadratic extension which trivialized 2-part of ideal class group

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