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

Author(s): Kay Rülling
Journal: J. Algebraic Geom. 16 (2007), 109-169.
Posted: July 24, 2006
Errata: J. Algebraic Geom. 16 (2007), 793-795
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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 CH$ ^n((\mathbb{A}^1_k,(m+1)\{0\}),n-1)$, $ n,m\ge1$. Bloch and Esnault prove CH$ ^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
Email: kay.ruelling@uni-essen.de

PII: S 1056-3911(06)00446-2
Received by editor(s): May 23, 2005
Posted: July 24, 2006
Additional Notes: The author was supported by the DFG Graduiertenkolleg 647.

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