Open Access
2013 Higher Chow groups of varieties with group action
Amalendu Krishna
Algebra Number Theory 7(2): 449-506 (2013). DOI: 10.2140/ant.2013.7.449


We give explicit descriptions of the higher Chow groups of toric bundles and flag bundles over schemes. We derive several consequences of these descriptions for the equivariant and ordinary higher Chow groups of schemes with group action.

We prove a decomposition theorem for the equivariant higher Chow groups of a smooth scheme with action of a diagonalizable group. This theorem is applied to compute the equivariant and ordinary higher Chow groups of smooth toric varieties. The results of this paper play fundamental roles in the proof of the Riemann–Roch theorems for equivariant higher K-theory.


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Amalendu Krishna. "Higher Chow groups of varieties with group action." Algebra Number Theory 7 (2) 449 - 506, 2013.


Received: 10 November 2011; Revised: 28 February 2012; Accepted: 28 March 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 06167126
MathSciNet: MR3123646
Digital Object Identifier: 10.2140/ant.2013.7.449

Primary: 14C35 , 14C40
Secondary: 14C25

Keywords: algebraic cycles , group action

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 2 • 2013
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