Cohen-Macaulay test ideals over rings of finite and countable Cohen-Macaulay type

DOI10.2140/involve.2021.14.413zbMath1471.13028arXiv2103.02529OpenAlexW3184962934MaRDI QIDQ2233360

Rebecca R. G., Julian Benali, Shrunal Pothagoni

Publication date: 18 October 2021

Published in: Involve (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.02529

zbMATH Keywords

test idealsmaximal Cohen-Macaulay modulesADE singularitiestrace ideals

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Cohen-Macaulay modules (13C14) Other commutative rings defined by combinatorial properties (13F70)

Cites Work

• Closure operations that induce big Cohen-Macaulay modules and classification of singularities
• Closure operations that induce big Cohen-Macaulay algebras
• Trace ideals, normalization chains, and endomorphism rings
• Geometric interpretation of tight closure and test ideals
• The multiplier ideal is a universal test ideal
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• Homological Algebra on a Complete Intersection, with an Application to Group Representations
• F-Regularity, Test Elements, and Smooth Base Change