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<p>We show that a pure transcendental, immediate extension of valuation rings <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(V\subset V'\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>V</mi> <mo>⊂</mo> <msup> <mi>V</mi> <mo>′</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> containing a field is a filtered union of smooth <i>V</i>-subalgebras of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(V'\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>V</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation>.</p>

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Pure transcendental, immediate valuation ring extensions as limits of smooth algebras

  • 期刊论文

  • 发表日期：

    2025年8月23日

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  • Dorin Popescu

摘要

We show that a pure transcendental, immediate extension of valuation rings \(V\subset V'\) V ⊂ V ′ containing a field is a filtered union of smooth V-subalgebras of \(V'\) V ′ .