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CHOW GROUPS, CHOW COHOMOLOGY, AND LINEAR VARIETIES

Part of: Cycles and subschemes (Co)homology theory Special varieties

Published online by Cambridge University Press:  24 June 2014

BURT TOTARO
BURT TOTARO*
Affiliation:
UCLA Mathematics Department, Box 951555, Los Angeles, CA 90095-1555, USA; totaro@math.ucla.edu

Abstract

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We compute the Chow groups and the Fulton–MacPherson operational Chow cohomology ring for a class of singular rational varieties including toric varieties. The computation is closely related to the weight filtration on the ordinary cohomology of these varieties. We use the computation to answer one of the open problems about operational Chow cohomology: it does not have a natural map to ordinary cohomology.

MSC classification

Secondary: 14C15: (Equivariant) Chow groups and rings; motives 14F42: Motivic cohomology; motivic homotopy theory 14M20: Rational and unirational varieties
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 2 , 01 July 2014 , e17
Creative Commons
Creative Common License - CCCreative Common License - BY
The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence .
Copyright
© The Author 2014

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