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
Full-text PDF

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.


References [Enhancements On Off] (What's this?)


Additional Information

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

DOI: https://doi.org/10.1090/S1056-3911-09-00521-9
Received by editor(s): May 31, 2008
Received by editor(s) in revised form: September 28, 2008
Published electronically: November 17, 2009

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
Comments: jag-query@ams.org
AMS Website