CHOW GROUPS OF COMPLETE REGULAR LOCAL RINGS III

Title & Authors
CHOW GROUPS OF COMPLETE REGULAR LOCAL RINGS III
Lee, Si-Chang;

Abstract
In this paper we will show that the followings ; (1) Let R be a regular local ring of dimension n. Then $\small{A_{n-2}}$(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 $\small{A_{n-3}}$(R). (3) Let R = V[[ $\small{X_1}$, $\small{X_2}$, …, $\small{X_{5}}$ ]]/(p+ $\small{X_1}$$\small{^{t1}}$ + $\small{X_2}$$\small{^{t2}}$ + $\small{X_3}$$\small{^{t3}}$ + $\small{X_4}$$\small{^2}$+ $\small{X_{5}}$ $\small{^2}$/), where p $\small{\neq}$2, $\small{t_1}$, $\small{t_2}$, $\small{t_3}$ 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.
Keywords
Chow group;complete regular local ring;Gorenstein ideal of codimension 3;dimension 5;height 3 ideal;
Language
English
Cited by
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