A solution to Itoh's conjecture for integral closure filtration

Let (A, m) be an analytically unramified Cohen-Macaulay local ring of dimension d 3 and let a be an m-primary ideal in A. If I is an ideal in A then let I^* be the integral closure of I in A. Let G₀ (A) ^* = ₍ ₀ (aⁿ) ^*/ (a^n+1) ^* be the associated graded ring of the integral closure filtration of a. Itoh conjectured in 1992 that if third Hilbert coefficient of G₀ (A) ^*, i. e. , e₃^a^* (A) = 0 and A is Gorenstein then G₀ (A) ^* is Cohen-Macaulay. In this paper we prove Itoh's conjecture (more generally for analytically unramified Cohen-Macaulay local rings).