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<p>The objective of this paper is to better understand <i>F</i>-injective thresholds and <i>F</i>-thresholds. Our approach is more general; we investigate the <i>F</i>-pure submodules of a module with a Cartier action, and relate their associated jumping numbers to numerical invariants of a Cartier algebra that resemble <i>F</i>-thresholds. As special cases, we obtain new results on the rationality and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathfrak {m}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">m</mi> </math></EquationSource> </InlineEquation>-adic constancy of <i>F</i>-injective thresholds and <i>F</i>-thresholds.</p>

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Jumping numbers of F-pure submodules

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月11日

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  • Alessandro De Stefani,
  • Daniel J. Hernández,
  • Luis Núñez-Betancourt,
  • Emily E. Witt

摘要

The objective of this paper is to better understand F-injective thresholds and F-thresholds. Our approach is more general; we investigate the F-pure submodules of a module with a Cartier action, and relate their associated jumping numbers to numerical invariants of a Cartier algebra that resemble F-thresholds. As special cases, we obtain new results on the rationality and \({\mathfrak {m}}\) m -adic constancy of F-injective thresholds and F-thresholds.