List questions from valuation-theory

Published on 27 Mar 2026 - 12:20

144

Views

Localization of a Polynomial ring Quotient over a DVR is a DVR

Published on 09 Jul 2022 - 10:16

274

Views

Neat way to show that $\mathbb{Z}_p$ is a principal ideal domain via inverse limit definition

Published on 14 Jul 2022 - 16:59

110

Views

What is the $ord_P$ function associated to $R$?

Published on 26 Mar 2026 - 21:07

142

Views

Neat way to prove that $\mathbb{Q}_p$ is complete via 'field of fractions of inverse limit' definition

Published on 15 Jul 2022 - 21:18

64

Views

Invariants of modules over principal ideal domains

Published on 27 Mar 2026 - 12:17

88

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Additional valuations on discretely valued field

Published on 19 Jul 2022 - 13:50

60

Views

Extending module homomorphisms into an injective cogenerator

Published on 28 Mar 2026 - 2:22

123

Views

Valuation rings of $k(x)$ when $k$ is algebraically closed

Published on 28 Jul 2022 - 7:26

163

Views

Valuations of $\mathbb Q_p$ with finite residue fields

Published on 03 Aug 2022 - 10:15

72

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Let $C$ be a curve and $P \in C$ a smooth point. Then the local ring $k[C]_P$ of $C$ at $P$ is a discret valuation ring.

Published on 05 Aug 2022 - 18:53

51

Views

Computing $\dim_K(K\otimes_A K)$ where $K$ is field of fractions of discrete valuation ring $A$

Published on 08 Aug 2022 - 18:44

50

Views

Tensor product of modules: $p^n\otimes m=0$ implies $m=0$

Published on 09 Aug 2022 - 18:18

89

Views

Projective object in an abelian category: how can I form a direct sum?

Published on 13 Aug 2022 - 13:42

123

Views

Reference needed: theory of modules over $\mathbb{Z}_p$

Published on 15 Aug 2022 - 11:06

List Question

Valuation of $\zeta-1$

Localization of a Polynomial ring Quotient over a DVR is a DVR

Neat way to show that $\mathbb{Z}_p$ is a principal ideal domain via inverse limit definition

What is the $ord_P$ function associated to $R$?

Neat way to prove that $\mathbb{Q}_p$ is complete via 'field of fractions of inverse limit' definition

Invariants of modules over principal ideal domains

Additional valuations on discretely valued field

Extending module homomorphisms into an injective cogenerator

Valuation rings of $k(x)$ when $k$ is algebraically closed

Valuations of $\mathbb Q_p$ with finite residue fields

Let $C$ be a curve and $P \in C$ a smooth point. Then the local ring $k[C]_P$ of $C$ at $P$ is a discret valuation ring.

Computing $\dim_K(K\otimes_A K)$ where $K$ is field of fractions of discrete valuation ring $A$

Tensor product of modules: $p^n\otimes m=0$ implies $m=0$

Projective object in an abelian category: how can I form a direct sum?

Reference needed: theory of modules over $\mathbb{Z}_p$

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