CHOW GROUPS OF COMPLETE REGULAR LOCAL RINGS III Lee, Si-Chang;
In this paper we will show that the followings ; (1) Let R be a regular local ring of dimension n. Then (R) = 0. (2) Let R be a regular local ring of dimension n and I be an ideal in R of height 3 such that R/I is a Gorenstein ring. Then [I] = 0 in (R). (3) Let R = V[[ , , …, ]]/(p+ + + + + /), where p 2, , , are arbitrary positive integers and V is a complete discrete valuation ring with (p) = mv. Assume that R/m is algebraically closed. Then all the Chow group for R is 0 except the last Chow group.group.oup.
Chow group;complete regular local ring;Gorenstein ideal of codimension 3;dimension 5;height 3 ideal;