List questions from algebraic-number-theory

Published on 14 Apr 2026 - 17:12

112

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Extension and contraction of ideals in rings of integers

Published on 16 Apr 2026 - 20:03

118

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Discriminant of a basis

Published on 09 Apr 2026 - 8:06

142

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Galois groups $G_{K^{nr}/K}$ and $G_{\bar{k}/k}$ identical (from Silverman's Arithmetic of EC)

Published on 14 Apr 2026 - 13:55

288

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Quadratic Reciprocity in quadratic number fields

Published on 17 Apr 2026 - 8:10

114

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What is the Chern class of a line bundle over a number ring?

Published on 09 Apr 2026 - 12:45

174

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Cancellation property holds in ideals in Dedekind domains

Published on 25 Mar 2026 - 16:13

69

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Let $K$ be an algebraic number field. Prove that $O_K$ contains infinitely many prime ideals.

Published on 15 Apr 2026 - 15:19

63

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Extending an absolute value via a limit of powers

Published on 28 Mar 2026 - 6:08

58

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Checking positivity of trace of a certain quaternion in $\mathbb{B}_{\ell,\infty}$

Published on 13 Apr 2026 - 15:08

323

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Let $P$ be a prime ideal in the ring of integers then $P \cap \Bbb Z$ is prime in $\Bbb Z$

Published on 14 Apr 2026 - 11:18

62

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Prove that there exist only finitely many integral ideals of $O_K$ to which $m$ belongs

Published on 15 Apr 2026 - 10:25

87

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Prove that $P_1,\cdots,P_r$ are distinct prime ideals of $O_K$ with $<p>=P_1^{e_1}\cdots P_r^{e_r}$ and $N(P_i)=p^{deg f_i},i=1,2,\cdots,r$

Published on 16 Apr 2026 - 16:16

625

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Suppose that the prime $p$ is totally ramified in $O_{K_1}$ and unramified in $O_{K_2}$. Prove that $K_1 \cap K_2=\Bbb Q$.

Published on 16 Apr 2026 - 8:28

157

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elliptic curve analogue of ambiguous class number formula

Published on 26 Mar 2026 - 12:35

List Question

Prime ideals $2 = p \cdot p'$

Extension and contraction of ideals in rings of integers

Discriminant of a basis

Galois groups $G_{K^{nr}/K}$ and $G_{\bar{k}/k}$ identical (from Silverman's Arithmetic of EC)

Quadratic Reciprocity in quadratic number fields

What is the Chern class of a line bundle over a number ring?

Cancellation property holds in ideals in Dedekind domains

Let $K$ be an algebraic number field. Prove that $O_K$ contains infinitely many prime ideals.

Extending an absolute value via a limit of powers

Checking positivity of trace of a certain quaternion in $\mathbb{B}_{\ell,\infty}$

Let $P$ be a prime ideal in the ring of integers then $P \cap \Bbb Z$ is prime in $\Bbb Z$

Prove that there exist only finitely many integral ideals of $O_K$ to which $m$ belongs

Prove that $P_1,\cdots,P_r$ are distinct prime ideals of $O_K$ with $<p>=P_1^{e_1}\cdots P_r^{e_r}$ and $N(P_i)=p^{deg f_i},i=1,2,\cdots,r$

Suppose that the prime $p$ is totally ramified in $O_{K_1}$ and unramified in $O_{K_2}$. Prove that $K_1 \cap K_2=\Bbb Q$.

elliptic curve analogue of ambiguous class number formula

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