Additive Chow groups

General Introduction
Classical (higher) Chow groups do not distinguish between a scheme and the associated reduced scheme. Additive (higher) Chow groups is a cohomology theory which should give a better notion of motivic cohomology for nonreduced schemes (for example truncated polynomial algebras such as the dual numbers). In particular, one hopes for an AtiyahHirzebruch spectral sequence from additive higher Chow groups to algebraic Ktheory.
Remark: As far as I can see, additive Chow groups have nothing to do with Additive Ktheory
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Online References
Key authors: Bloch, Esnault, Rülling, Park, Krishna, Levine.
Krishna and Levine: Additive Chow groups of schemes
Bloch: Additive Chow groups and algebraic cycles
Bloch and Esnault: An additive version of higher Chow groups, The additive dilogarithm
Various articles of Jinhyun Park
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
arXiv:0909.3155 Moving Lemma for additive Chow groups and applications from arXiv Front: math.AG by Amalendu Krishna, Jinhyun Park We prove moving lemma for additive higher Chow groups of smooth projective varieties. As applications, we prove the very general contravariance property of additive higher Chow groups. Using the moving lemma, we establish the structure of gradedcommutative differential graded algebra (CDGA) on these groups.
arXiv:1208.6455 Somekawa's $K$groups and additive higher Chow groups from arXiv Front: math.KT by Toshiro Hiranouchi We introduce the Milnor type $K$group attached to some algebraic groups including Witt groups over a perfect field as an extension of Somekawa's $K$group. We give a description of this $K$group associated to the additive group and the multiplicative group by the space of the absolute Kähler differentials, and relate also our Somekawa $K$group for the additive group and the Jacobian variety of a curve with a complex determined by the residue maps and the trace maps. The same arguments work for the Mackey product of the additive higher Chow group and the higher Chow group for a scheme. This gives vanishing results of additive Chow groups on zerocycles.
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