ON CHOW GROUPS OF COMPLETE REGULAR LOCAL RINGS

摘要

In this paper, we establish the validity of the Chow group problem for complete regular local rings R of dimension up to 4. For dimension n (＞ 4) over ramified regular local ring R, we have two results: (1) When / is an ideal of height 3 such that R/I is a Gorenstein ring, then [I] = 0 in A_(n-3)(R). (2) We reduce any prime ideal of height i to an almost complete intersection ideal of height i and in some special cases of almost complete intersection ideal of height i, we show that all Chow groups except the top one vanish. A necessary and sufficient condition for the vanishing of Chow groups is also derived using Eisenstein extension.