Localization of tight closure in two-dimensional rings
  It is shown that tight closure commutes with localization in any two dimensional ring $R$ of prime characteristic if either $R$ is a Nagata ring or $R$ possesses a weak test element. Moreover, it is proved that tight closure commutes with localization at height one prime ideals in any ring of prime characteristic. 
Kamran Divaani-Aazar and Massoud Tousi