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Winter 2012 On Chow groups of complete regular local rings
Sichang Lee
Illinois J. Math. 56(4): 1085-1093 (Winter 2012). DOI: 10.1215/ijm/1399395823


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.


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Sichang Lee. "On Chow groups of complete regular local rings." Illinois J. Math. 56 (4) 1085 - 1093, Winter 2012.


Published: Winter 2012
First available in Project Euclid: 6 May 2014

zbMATH: 1295.13033
MathSciNet: MR3231474
Digital Object Identifier: 10.1215/ijm/1399395823

Primary: 13D45, 13H05

Rights: Copyright © 2012 University of Illinois at Urbana-Champaign


Vol.56 • No. 4 • Winter 2012
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