Algebra & Number Theory

Higher Chow groups of varieties with group action

Amalendu Krishna

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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.

Article information

Source
Algebra Number Theory, Volume 7, Number 2 (2013), 449-506.

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513729950

Digital Object Identifier
doi:10.2140/ant.2013.7.449

Mathematical Reviews number (MathSciNet)
MR3123646

Zentralblatt MATH identifier
06167126

Subjects
Primary: 14C40: Riemann-Roch theorems [See also 19E20, 19L10] 14C35: Applications of methods of algebraic $K$-theory [See also 19Exx]
Secondary: 14C25: Algebraic cycles

Keywords
algebraic cycles group action

Citation

Krishna, Amalendu. Higher Chow groups of varieties with group action. Algebra Number Theory 7 (2013), no. 2, 449--506. doi:10.2140/ant.2013.7.449. https://projecteuclid.org/euclid.ant/1513729950


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