Gersten's conjecture for K_0-groups, by Satoshi Mochizuki

[A cautionary note has been added by the author, June 11, 2007.]

This paper is an extended version of No. 837.

In this paper, we will propse a generalized Gersten's conjectue for Cohen-Macaulay local rings and prove that this conjecture for K_0-groups is true. As its application, we will obtain the vanishing conjecture for certain Chow groups and generators conjecture for certain K-groups.

Caution:

In this paper, there are several mistakes. The main reason is the error in the proof of claim 2 in proposition 1.3.

The author is using the approximation criterion of Thomason-Trobaugh 1.9.5 to bounded complexes. But in general, the criterion is only working on cohomologically bounded complexes.

For example, let R be a discrete valuation ring and x its prime element and put I=(x^2). Then R/x does not have a finite resolution as a R/I-module.

And as in Paul Balmer's paper No. 849, there is a counterexample of the assertion in Corollary 2.6.

Acknowlegement: The author is thankful to Charles A. Weibel for pointing out a mistake in the preprint and to Paul Balmer for teaching the counterexample.


Satoshi Mochizuki <mochi81@hotmail.com>