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 Gₐ(A)^* = n≥ 0(aⁿ)^*/(aⁿ⁺¹)^* be the associated graded ring of the integral closure filtration of a. Itoh conjectured in 1992 that if third Hilbert coefficient of Gₐ(A)^* , i.e., e₃a^*(A) = 0 and A is Gorenstein then Gₐ(A)^* is Cohen-Macaulay. In this paper we prove Itoh's conjecture (more generally for analytically unramified Cohen-Macaulay local rings).