List questions from valuation-theory

Published on 14 Apr 2026 - 19:56

695

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What are the discrete valuation rings for the affine plane?

Published on 06 May 2026 - 14:28

156

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Example of the set of absolute value on number fields.

Published on 15 Apr 2026 - 21:03

171

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In valued fields (of rank > 1), is the p-adic completion of the algebraic closure still algebraically closed?

Published on 16 Apr 2026 - 5:34

610

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absolute value and valuation on the field of formal power series

Published on 15 Apr 2026 - 10:47

58

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Discrete valuation arising from localizations of $R[[t]]$

Published on 15 Apr 2026 - 10:34

110

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Immediate extension of valuation on an algebraically closed field is determined by cofinal sequence.

Published on 14 Apr 2026 - 10:44

235

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Continuity of trace and norm

Published on 09 Apr 2026 - 21:57

490

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discrete multiplicative subgroup of the reals are cyclic

Published on 15 Apr 2026 - 2:56

174

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Valuation ring of $K(\alpha)$ is $A[\alpha]$?

Published on 16 Apr 2026 - 0:43

127

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Why $B\otimes_A \hat A\backsimeq \prod_{\mathfrak q|\mathfrak p}\hat B_\mathfrak q$ if they are isomorphic after reducing modulo $\hat{\mathfrak p}$?

Published on 15 Apr 2026 - 20:39

368

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Equivalent Valuations

Published on 30 Apr 2026 - 11:28

72

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Theorem of independence (discrete valuation)

Published on 11 Apr 2026 - 9:50

194

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$(\varphi,\Gamma)$-modules and valuation in Zp

Published on 15 Apr 2026 - 22:43

1.3k

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Computing quotient by dividing formally in $p$-adic number system

Published on 12 Apr 2026 - 18:09

List Question

Does totally ordered prime ideals in a domain imply valuation ring?

What are the discrete valuation rings for the affine plane?

Example of the set of absolute value on number fields.

In valued fields (of rank > 1), is the p-adic completion of the algebraic closure still algebraically closed?

absolute value and valuation on the field of formal power series

Discrete valuation arising from localizations of $R[[t]]$

Immediate extension of valuation on an algebraically closed field is determined by cofinal sequence.

Continuity of trace and norm

discrete multiplicative subgroup of the reals are cyclic

Valuation ring of $K(\alpha)$ is $A[\alpha]$?

Why $B\otimes_A \hat A\backsimeq \prod_{\mathfrak q|\mathfrak p}\hat B_\mathfrak q$ if they are isomorphic after reducing modulo $\hat{\mathfrak p}$?

Equivalent Valuations

Theorem of independence (discrete valuation)

$(\varphi,\Gamma)$-modules and valuation in Zp

Computing quotient by dividing formally in $p$-adic number system

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