Closure operations that induce big Cohen-Macaulay algebras

DOI10.1016/j.jpaa.2017.08.011zbMath1470.13033arXiv1512.07862OpenAlexW2963119762MaRDI QIDQ1703599

Rebecca R. G.

Publication date: 2 March 2018

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.07862

zbMATH Keywords

test idealtight closurebig Cohen-Macaulay algebraDietz closure

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 (7)

Existence of almost Cohen-Macaulay algebras implies the existence of big Cohen-Macaulay algebras ⋮ Closure operations in complete local rings of mixed characteristic ⋮ Tight closure and strongly F-regular rings ⋮ Axiomatic closure operations, phantom extensions, and solidity ⋮ Cohen-Macaulay test ideals over rings of finite and countable Cohen-Macaulay type ⋮ Characteristic-free test ideals ⋮ Big Cohen-Macaulay and seed algebras in equal characteristic zero via ultraproducts

Cites Work

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• Closure operations that induce big Cohen-Macaulay modules and classification of singularities
• Absolute integral closure in positive characteristic
• Infinite integral extensions and big Cohen-Macaulay algebras
• Big Cohen-Macaulay algebras and the vanishing conjecture for maps of Tor in mixed characteristic
• The direct factor conjecture
• Axiomatic closure operations, phantom extensions, and solidity
• The direct summand conjecture in dimension three.
• Big Cohen-Macaulay algebras in dimension three via Heitmann's theorem.
• Applications of the existence of big Cohen-Macaulay algebras
• Canonical elements in local cohomology modules and the direct summand conjecture
• Big Cohen-Macaulay and seed algebras in equal characteristic zero via ultraproducts
• Lefschetz extensions, tight closure and big Cohen-Macaulay algebras
• A guide to closure operations in commutative algebra
• A survey of test ideals
• A characterization of closure operations that induce big Cohen-Macaulay modules
• Big Cohen-Macaulay algebras and seeds
• Contracted ideals from integral extensions of regular rings

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