A tight closure approach to arithmetic Macaulayfication (Q1922061)

Here is the main result of this paper: Let \(R\) be an excellent normal local ring of prime characteristic and of dimension \(d\). Let \(J\) be an ideal generated of a system of parameters which are test elements (as defined in the theory of tight closure). Then the Rees algebra \(R[Jt]\) is Cohen-Macaulay. This theorem implies the existence of an arithmetic Macaulayfication if \(R\) has an isolated non-\(F\)-rational point, in particular, if \(R\) has an isolated singularity. The existence of an arithmetic Macaylayfication in the case of an isolated singularity follows from the work of M. Brodmann and of S. Goto and K. Yamagishi. However, the methods of this paper are different. The authors use tight closure, especially some variant of ``colon-capturing''.