2015/04/11 by Phạm Hùng Quý, Pham Hung Quy, Quy, Pham Hung · 1 citation
Mathematics · #13A35 #13B40 #13D22 #13D45 #13H10 #14B15 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AC #math.AG #msc:13A35 #msc:13B40 #msc:13D22 #msc:13D45 #msc:13H10 #msc:14B15
paper · pdf · doi:10.48550/arxiv.1504.02925
to appear in Journal of Algebra
openalex publication_date 2015/04/11 · arxiv created 2016/03/14 · arxiv updated 2016/03/15 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
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 R be 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 R is 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.