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    Title      l  Moving lemma for additive Chow groups and applications
    Author   l  Amalendu Krishna and Jinhyun Park
    Date   l  2009-09-18
    Category   l  ASARC-Preprint-09-24
    Download    l 1253261267_0.612489.pdf  
Abstract. We study additive higher Chow groups with several modulus conditions.
Apart from exhibiting the validity of all known results for the additiveChow groups
with these modulus conditions, we prove the moving lemma forthem: for a smooth
projective variety X and a nite collection W of its locallyclosed 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 applications, we show that any map from a quasi-projective variety to a smooth
projective variety induces a pull-back map of additive higher Chow groups.
Using the moving lemma, we also establish the structure of gradedcommutative
dierential graded algebra (CDGA) on the additive higher Chow groups.

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