چکیده (انگلیسی):

The aim of this paper is to extend the main result of C. Huneke and G. Lyubeznik in [Adv. Math. 210 (2007), 498–504] to the class of rings that are images of Cohen–Macaulay local rings. Namely, let Rbe a local Noetherian domain of positive characteristic that is an image of a Cohen–Macaulay local ring. We prove that all local cohomology of R(below the dimension) maps to zero in a finite extension of the ring. As a direct consequence we obtain that the absolute integral closure of Ris a big Cohen–Macaulay algebra. Since every excellent local ring is an image of a Cohen–Macaulay local ring, this result is a generalization of the main result of M.Hochster and Huneke in [Ann. of Math. 135 (1992), 45–79] with a simpler proof.