Vol. 6, No. 2, 2012

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Moving lemma for additive higher Chow groups

Amalendu Krishna and Jinhyun Park

Vol. 6 (2012), No. 2, 293–326

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.

Chow group, algebraic cycle, moving lemma
Mathematical Subject Classification 2000
Primary: 14C25
Secondary: 19E15
Received: 30 May 2010
Revised: 9 January 2011
Accepted: 6 February 2011
Published: 24 June 2012
Amalendu Krishna
School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road, Colaba
Jinhyun Park
Department of Mathematical Sciences
Korea Advanced Institute of Science and Technology
291 Daehak-ro, Yuseong-gu
Daejeon 305-701
South Korea