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Regulators on additive higher Chow groups

Jinhyun Park
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Abstract

As an attempt to understand motives over $k[x]/(x^m)$, we define the cubical additive higher Chow groups with modulus for all dimensions extending the works of S. Bloch, H. Esnault and K. Rülling on 0-dimensional cycles. We give an explicit construction of regulator maps on the groups of 1-cycles with an aid of the residue theory of A. Parshin and V. Lomadze.

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Jinhyun Park. 2008-05-28. Regulators on additive higher Chow groups. https://arxiv.org/abs/math/0605702

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