On Macaulayfication of Noetherian schemes

By T. Kawasaki. 2000

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On arithmetic Macaulayfication of Noetherian rings (2001, background): “The next proposition is not in [ 17 ] but we need it to prove Theorem 1.1.”
Local cohomology based on a nonclosed support defined by a pair of ideals (2007, background): “Proof. In virtue of [ 13, Theorem 1.2 ] we can take a Gorenstein ring A of dimension r with a surjective ring homomorphism φ : A → R/Ann M. Replacing R (resp.”
Homological invariants associated to semi-dualizing bimodules (2005, background): “The remaining implication (6) ⇒ (1) that is the most difficult to prove follows from [ 11, Theorem 1.2 ].”
Extensions of a dualizing complex by its ring: commutative versions of a conjecture of Tachikawa (2002, background): “completeness, we recall that this is the case if and only if R is a homomorphic image of a Gorenstein ring, where the “if” part is a deep recent result of Kawasaki [ 27 ].”