A Property of the Absolute Integral Closure of an Excellent Local Domain in Mixed Characteristic

摘要

Let (R, m) be a Noetherian local excellent domain and let R~+ be the absolute integral closure of R-that is, the integral closure of R in the algebraic closure of the fraction field of R. The ring R~+ when R is 3-dimensional and of mixed characteristic played an important role in Heitmann's proof of the direct summand conjecture in dimension 3 [3]. In dimension > 3 the direct summand conjecture is still open. This motivates the study of R~+ in mixed characteristic and in dimension > 3.