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. R\"ulling 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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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 257-276
Launched on MUSE
2009-01-30
Open Access
No
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