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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Higher bivariant Chow groups and motivic filtrations


Author: Abhishek Banerjee
Journal: Trans. Amer. Math. Soc. 363 (2011), 5943-5969
MSC (2010): Primary 14C15, 14C25
Published electronically: May 25, 2011
MathSciNet review: 2817416
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Abstract: The purpose of this paper is twofold: first, we extend Saito's filtration on Chow groups, which is a candidate for the conjectural Bloch Beilinson filtration on the Chow groups of a smooth projective variety, from Chow groups to the bivariant Chow groups. In order to do this, we construct cycle class maps from the bivariant Chow groups to bivariant cohomology groups. Secondly, we use our methods to define a bivariant version of Bloch's higher Chow groups.


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Additional Information

Abhishek Banerjee
Affiliation: Institut des Hautes Études Scientifiques, Le Bois-Marie 35, Route de Chartres 91440, Bures sur Yvette, France
Address at time of publication: Department of Mathematics, Ohio State University, 231 W. 18th Avenue, 100 Math Tower, Columbus, Ohio 43210
Email: abhishekbanerjee1313@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05300-6
PII: S 0002-9947(2011)05300-6
Received by editor(s): September 19, 2009
Received by editor(s) in revised form: January 16, 2010
Published electronically: May 25, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.