Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

An Artin-Rees theorem in $K$-theory and applications to zero cycles


Author: Amalendu Krishna
Journal: J. Algebraic Geom. 19 (2010), 555-598
DOI: https://doi.org/10.1090/S1056-3911-09-00521-9
Published electronically: November 17, 2009
MathSciNet review: 2629600
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Abstract | References | Additional Information

Abstract:

For the smooth normalization $f : {\overline X} \to X$ of a singular variety $X$ over a field $k$ of characteristic zero, we show that for any conducting subscheme $Y$ for the normalization, and for any $i \in \mathbb {Z}$, the natural map $K_i(X, {\overline X}, nY) \to K_i(X, {\overline X}, Y)$ is zero for all sufficiently large $n$.

As an application, we prove a formula for the Chow group of zero cycles on a quasi-projective variety $X$ over $k$ with Cohen-Macaulay isolated singularities, in terms of an inverse limit of the relative Chow groups of a desingularization $\widetilde X$ relative to the multiples of the exceptional divisor.

We use this formula to verify a conjecture of Srinivas about the Chow group of zero cycles on the affine cone over a smooth projective variety which is arithmetically Cohen-Macaulay.


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Additional Information

Amalendu Krishna
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005 India
MR Author ID: 703987
Email: amal@math.tifr.res.in

Received by editor(s): May 31, 2008
Received by editor(s) in revised form: September 28, 2008
Published electronically: November 17, 2009