Parameter test ideals of Cohen Macaulay rings

Abstract

We describe an algorithm for computing parameter-test-ideals in certain local Cohen-Macaulay rings. The algorithm is based on the study of a Frobenius map on the injective hull of the residue field of the ring and on the application of Rodney Sharp's notion of ``special ideals''. Our techniques also provide an algorithm for computing indices of nilpotency of Frobenius actions on top local cohomology modules of the ring and on the injective hull of its residue field. The study of nilpotent elements on injective hulls of residue fields also yields a great simplification of the proof of the fact that for a power series ring $R$ of prime characteristic, for all nonzero $f\in R$, $1/f$ generates $R_f$ as a $D_R$-module.

16 pages To appear in Compositio Mathematica

References in corpus (2)

• Parameter test ideals of Cohen Macaulay rings
• The intersection homology D--module in finite characteristic

Cited by in corpus (21)

• Parameter test ideals of Cohen Macaulay rings
• A survey of test ideals
• Test ideals of non-principal ideals: Computations, Jumping Numbers, Alterations and Division Theorems
• Frobenius maps on injective hulls and their applications to tight closure
• Right and Left Modules over the Frobenius Skew Polynomial Ring in the F-Finite Case
• F-singularities in families
• On the upper semi-continuity of HSL numbers
• On the discreteness and rationality of F-jumping coefficients
• An algorithm for producing F-pure ideals
• Local m-adic constancy of F-pure thresholds and test ideals
• The TestIdeals package for Macaulay2
• Estimates for F-jumping numbers and bounds for Hartshorne-Speiser-Lyubeznik numbers
• Graded annihilators and tight closure test ideals
• An algorithm for computing compatibly Frobenius split subvarieties
• The support of local cohomology modules
• Global parameter test ideals
• An excellent F-pure ring of prime characteristic has a big tight closure test element
• A non-finitely generated algebra of Frobenius maps
• Multiplicity bounds in prime characteristic
• Annihilators of Artinian modules compatible with a Frobenius map
• The level of pairs of polynomials