List questions from valuation-theory

Published on 26 Mar 2026 - 6:04

870

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Possible valuations on polynomial ring

Published on 24 Aug 2017 - 7:05

1.9k

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How to show the only absolute value on a finite field is the trivial one.

Published on 30 Aug 2017 - 0:31

232

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Discrete valuation on the local ring of a nonsingular curve

Published on 05 Sep 2017 - 14:47

55

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$|b|^{\frac {1}{\log b}}= |a|^{\frac {1}{\log a}}$ implies $|b|=b^ {\lambda}$

Published on 26 Mar 2026 - 21:07

435

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Extension of $\mathfrak{p}$-adic valuation

Published on 26 Mar 2026 - 19:07

579

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Can we have a perfect field of characteristic $p$ with a non-archimedean valuation?

Published on 29 Sep 2017 - 16:54

110

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Why is the order of $A/m$ is $p^f$?

Published on 13 Oct 2017 - 20:01

239

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Polynomial with coefficients 'sufficiently close' to irreducible polynomial is irreducible

Published on 14 Oct 2017 - 14:12

310

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Valuation ring and field extension

Published on 19 Oct 2017 - 1:43

556

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Almost a discrete valuation ring

Published on 23 Oct 2017 - 15:32

58

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"Sufficiently close" Ring Extensions

Published on 25 Oct 2017 - 9:44

97

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Let $A$ be a Dedekind domain and $p$ be a prime ideal in $A$ then how to prove that $A/p^n \equiv A_p/p^nA_p$.

Published on 26 Mar 2026 - 23:10

787

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How to recover a divisor from its valuation (Hartshorne II.6 and ex. II.4.5)

Published on 30 Nov 2017 - 6:21

750

Views

Absolute values equivalence in $\mathbb{F}_{q}(x)$

Published on 02 Dec 2017 - 23:36

List Question

Blow up along a valuation

Possible valuations on polynomial ring

How to show the only absolute value on a finite field is the trivial one.

Discrete valuation on the local ring of a nonsingular curve

$|b|^{\frac {1}{\log b}}= |a|^{\frac {1}{\log a}}$ implies $|b|=b^ {\lambda}$

Extension of $\mathfrak{p}$-adic valuation

Can we have a perfect field of characteristic $p$ with a non-archimedean valuation?

Why is the order of $A/m$ is $p^f$?

Polynomial with coefficients 'sufficiently close' to irreducible polynomial is irreducible

Valuation ring and field extension

Almost a discrete valuation ring

"Sufficiently close" Ring Extensions

Let $A$ be a Dedekind domain and $p$ be a prime ideal in $A$ then how to prove that $A/p^n \equiv A_p/p^nA_p$.

How to recover a divisor from its valuation (Hartshorne II.6 and ex. II.4.5)

Absolute values equivalence in $\mathbb{F}_{q}(x)$

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