Higher Chow groups of varieties with group action

Krishna, Amalendu

doi:10.2140/ant.2013.7.449

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Higher Chow groups of varieties with group action

Amalendu Krishna

Vol. 7 (2013), No. 2, 449–506

DOI: 10.2140/ant.2013.7.449

Abstract

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.

Keywords

algebraic cycles, group action

Mathematical Subject Classification 2010

Primary: 14C40, 14C35

Secondary: 14C25

Milestones

Received: 10 November 2011

Revised: 28 February 2012

Accepted: 28 March 2012

Published: 25 April 2013

Authors

Amalendu Krishna
School of Mathematics Tata Institute of Fundamental Research 1 Homi Bhabha Road Mumbai 400005 India

Vol. 7, No. 2, 2013