Higher bivariant Chow groups and motivic filtrations

Banerjee, Abhishek

doi:10.1090/S0002-9947-2011-05300-6

Higher bivariant Chow groups and motivic filtrations
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by Abhishek Banerjee

Trans. Amer. Math. Soc. 363 (2011), 5943-5969

DOI: https://doi.org/10.1090/S0002-9947-2011-05300-6

Published electronically: May 25, 2011

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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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