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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



The generalized de Rham-Witt complex over a field is a complex of zero-cycles

Author: Kay Rülling
Journal: J. Algebraic Geom. 16 (2007), 109-169
Published electronically: July 24, 2006
Erratum: J. Algebraic Geom. 16 (2007), 793-795.
MathSciNet review: 2257322
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Abstract | References | Additional Information

Abstract: Bloch and Esnault defined additive higher Chow groups with modulus $m$ on the level of zero cycles over a field $k$ denoted by $\text {CH}^n((\mathbb {A}^1_k,(m+1)\{0\}),n-1)$, $n,m\ge 1$. Bloch and Esnault prove $\text {CH}^n((\mathbb {A}^1_k,2\{0\}),n-1)\cong \Omega ^{n-1}_{k/\mathbb {Z}}$. In this paper we generalize their result and prove that the additive Chow groups with higher modulus form a generalized Witt complex over $k$ and are as such isomorphic to the generalized de Rham-Witt complex of Bloch-Deligne-Hesselholt-Illusie-Madsen.

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Additional Information

Kay Rülling
Affiliation: Universität Duisburg-Essen, Essen, FB6, Mathematik, 45117 Essen, Germany

Received by editor(s): May 23, 2005
Published electronically: July 24, 2006
Additional Notes: The author was supported by the DFG Graduiertenkolleg 647.