List questions from class-field-theory

Published on 24 Mar 2026 - 11:41

70

Views

Is $h(n) < 2^n$ for all $n$? ($n$th cyclotomic field class number growth)

Published on 25 Mar 2026 - 1:17

138

Views

Non-Galois finite extensions of $F^{\operatorname{ur}}$

Published on 25 Mar 2026 - 4:42

143

Views

Minkowski bound of $229$-th cyclotomic field

Published on 24 Mar 2026 - 22:01

308

Views

Vanishing of second Galois cohomology group

Published on 25 Mar 2026 - 6:35

185

Views

$p >2$ is a prime, any facts about congruence relation between the class number of $Q(\sqrt p)$ and $Q(\sqrt{-p})$?

Published on 03 Aug 2018 - 14:26

371

Views

Artin symbol property

Published on 10 Aug 2018 - 0:00

208

Views

About the definition of local fields

Published on 15 Aug 2018 - 4:49

45

Views

Why is $EK_w$ complete?

Published on 21 Aug 2018 - 5:06

140

Views

Extensions of Hilbert class fields

Published on 07 Sep 2018 - 15:59

159

Views

If $\alpha^3+4k\alpha-k=0$ with $k\geq 1$ is odd, then $\mathbb{Q}(\alpha)$ has even class number.

Published on 10 Sep 2018 - 18:19

526

Views

Local Kronecker–Weber theorem implies the global one?

Published on 11 Sep 2018 - 15:03

80

Views

Under What assumptions on $p$, $\mathcal{O}_K^* \simeq \mathbb{Z}_p^{} \oplus \mathbb{Z}_p^{}$

Published on 25 Mar 2026 - 3:07

152

Views

Absolute value of tensor product of fields

Published on 20 Sep 2018 - 16:45

63

Views

Why $\mathbb Q_p(\xi_n) = \mathbb Q_p$ implies $n|(p-1)$.

Published on 01 Oct 2018 - 15:09

List Question

When does a number field have $p$-rank greater than $n$?

Is $h(n) < 2^n$ for all $n$? ($n$th cyclotomic field class number growth)

Non-Galois finite extensions of $F^{\operatorname{ur}}$

Minkowski bound of $229$-th cyclotomic field

Vanishing of second Galois cohomology group

$p >2$ is a prime, any facts about congruence relation between the class number of $Q(\sqrt p)$ and $Q(\sqrt{-p})$?

Artin symbol property

About the definition of local fields

Why is $EK_w$ complete?

Extensions of Hilbert class fields

If $\alpha^3+4k\alpha-k=0$ with $k\geq 1$ is odd, then $\mathbb{Q}(\alpha)$ has even class number.

Local Kronecker–Weber theorem implies the global one?

Under What assumptions on $p$, $\mathcal{O}_K^* \simeq \mathbb{Z}_p^{} \oplus \mathbb{Z}_p^{}$

Absolute value of tensor product of fields

Why $\mathbb Q_p(\xi_n) = \mathbb Q_p$ implies $n|(p-1)$.

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