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<p>We investigate the existence of almost p-standard systems of parameters under flat base change. For a faithfully flat homomorphism of Noetherian local rings <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R\rightarrow S\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mo stretchy="false">→</mo> <mi>S</mi> </mrow> </math></EquationSource> </InlineEquation> with a Cohen–Macaulay special fiber, we show that the existence of such a system of parameters on <i>R</i> implies its existence on <i>S</i>. As applications, we give precise relationships between various invariants such as the Cohen–Macaulay defect, length function, and Hilbert coefficients relative to almost p-standard systems of parameters of a module over <i>R</i> and its base change over <i>S</i>.</p>

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Flat Base Change of Almost p-Standard System of Parameters and Applications

  • 期刊论文

  • 发表日期：

    2026年3月28日

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  • Đoàn Trung Cường,
  • Phạm Hồng Nam

摘要

We investigate the existence of almost p-standard systems of parameters under flat base change. For a faithfully flat homomorphism of Noetherian local rings \(R\rightarrow S\) R → S with a Cohen–Macaulay special fiber, we show that the existence of such a system of parameters on R implies its existence on S. As applications, we give precise relationships between various invariants such as the Cohen–Macaulay defect, length function, and Hilbert coefficients relative to almost p-standard systems of parameters of a module over R and its base change over S.