Moving lemma for additive higher Chow groups

Krishna, Amalendu; Park, Jinhyun

doi:10.2140/ant.2012.6.293

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Moving lemma for additive higher Chow groups

Amalendu Krishna and Jinhyun Park

Vol. 6 (2012), No. 2, 293–326

DOI: 10.2140/ant.2012.6.293

Abstract

We study additive higher Chow groups with several modulus conditions. Apart from exhibiting the validity of all known results for the additive Chow groups with these modulus conditions, we prove the moving lemma for them: for a smooth projective variety $X$ and a finite collection $W$ of its locally closed algebraic subsets, every additive higher Chow cycle is congruent to an admissible cycle intersecting properly all members of $W$ times faces. This is the additive analogue of the moving lemma for the higher Chow groups studied by S. Bloch and M. Levine.

As an application, we prove that any morphism from a quasiprojective variety to a smooth projective variety induces a pull-back map of additive higher Chow groups. More important applications of this moving lemma are derived in two separate papers by the authors.

Keywords

Chow group, algebraic cycle, moving lemma

Mathematical Subject Classification 2000

Primary: 14C25

Secondary: 19E15

Milestones

Received: 30 May 2010

Revised: 9 January 2011

Accepted: 6 February 2011

Published: 24 June 2012

Authors

Amalendu Krishna
School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road, Colaba Mumbai-400005 India

Jinhyun Park
Department of Mathematical Sciences Korea Advanced Institute of Science and Technology 291 Daehak-ro, Yuseong-gu Daejeon 305-701 South Korea

Vol. 6, No. 2, 2012