Closure operations that induce big Cohen-Macaulay modules and classification of singularities

DOI10.1016/j.jalgebra.2016.08.009zbMath1401.13031arXiv1512.06843OpenAlexW2337014631MaRDI QIDQ314249

Rebecca R. G.

Publication date: 13 September 2016

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.06843

zbMATH Keywords

closure operationscommutative algebrabig Cohen-Macaulay moduleshomological conjectures

Mathematics Subject Classification ID

Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Homological conjectures (intersection theorems) in commutative ring theory (13D22) Cohen-Macaulay modules (13C14)

Related Items (8)

Closure operations in complete local rings of mixed characteristic ⋮ Tight closure and strongly F-regular rings ⋮ Closure operations that induce big Cohen-Macaulay algebras ⋮ Axiomatic closure operations, phantom extensions, and solidity ⋮ Cohen-Macaulay test ideals over rings of finite and countable Cohen-Macaulay type ⋮ Closure-interior duality over complete local rings ⋮ Characteristic-free test ideals ⋮ Nakayama closures, interior operations, and core-hull duality -- with applications to tight closure theory

Cites Work

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• Canonical elements in local cohomology modules and the direct summand conjecture
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• A characterization of closure operations that induce big Cohen-Macaulay modules
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• Cyclic Purity Versus Purity in Excellent Noetherian Rings
• Regular closure
• F-Regularity, Test Elements, and Smooth Base Change
• Phantom homology
• Contracted ideals from integral extensions of regular rings

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