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
DOI: https://doi.org/10.1090/S1056-3911-06-00446-2
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 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

DOI: https://doi.org/10.1090/S1056-3911-06-00446-2
Received by editor(s): May 23, 2005
Published electronically: July 24, 2006
Additional Notes: The author was supported by the DFG Graduiertenkolleg 647.

American Mathematical Society