Finite Tor dimension and failure of coherence in absolute integral closures

DOI10.1016/S0022-4049(97)00049-2zbMath0908.13006MaRDI QIDQ1376298

Melvin Hochster, Ian M. Aberbach

Publication date: 18 March 1999

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

zbMATH Keywords

characteristic \(p\)tight closureradicalFrobenius endomorphismintegral closureperfect ringTor dimension

Mathematics Subject Classification ID

Homological dimension and commutative rings (13D05) Integral closure of commutative rings and ideals (13B22) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

Related Items (10)

Coherence of absolute integral closures ⋮ Absolute integral closure in positive characteristic ⋮ Projectivity of the Witt vector affine Grassmannian ⋮ Vanishing of Tors of absolute integral closures in equicharacteristic zero ⋮ Almost Cohen-Macaulay and almost regular algebras via almost flat extensions ⋮ Regular rings and perfect(oid) algebras ⋮ F-coherent rings with applications to tight closure theory ⋮ Homological properties of the perfect and absolute integral closures of noetherian domains ⋮ Universally Going-Down Rings, 1-Split Rings, and Absolute Integral Closure ⋮ On the notion of Cohen-Macaulayness for non-Noetherian rings

Cites Work

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• Commutative coherent rings
• Infinite integral extensions and big Cohen-Macaulay algebras
• Tight closure of parameter ideals
• Applications of the existence of big Cohen-Macaulay algebras
• Canonical elements in local cohomology modules and the direct summand conjecture
• Rational singularities, with applications to algebraic surfaces and unique factorization
• On the joints of Hensel rings
• Some Numerical Criteria for Contractability of Curves on Algebraic Surfaces
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• Localization of tight closure and modules of finite phantom projective dimension.
• Finite Phantom Projective Dimension
• Tight closure in F-rational rings

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