## Illinois Journal of Mathematics

### On Chow groups of complete regular local rings

Sichang Lee

#### Abstract

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 $I$ 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.

#### Article information

Source
Illinois J. Math., Volume 56, Number 4 (2012), 1085-1093.

Dates
First available in Project Euclid: 6 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1399395823

Digital Object Identifier
doi:10.1215/ijm/1399395823

Mathematical Reviews number (MathSciNet)
MR3231474

Zentralblatt MATH identifier
1295.13033

#### Citation

Lee, Sichang. On Chow groups of complete regular local rings. Illinois J. Math. 56 (2012), no. 4, 1085--1093. doi:10.1215/ijm/1399395823. https://projecteuclid.org/euclid.ijm/1399395823

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