Mixed motives over \(k[t]/(t^{m+1})\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 1246.14017
DOI: 10.1017/S1474748011000181
author: Amalendu Krishna
author: Jinhyun Park
published in: Journal of the Institute of Mathematics of Jussieu
publication date: 2012-06-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1001.5112
Mathematics Subject Classification ID: 14C25
Mathematics Subject Classification ID: 19E15
zbMATH DE Number: 6051264
zbMATH Keywords: Chow group
zbMATH Keywords: algebraic cycle
zbMATH Keywords: moving lemma
zbMATH Keywords: motive
MaRDI profile type: Publication
arXiv ID: 1001.5112
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OpenAlex ID: W2964189847
title: Mixed motives over \(k[t]/(t^{m+1})\)
review text: Let \(k\) be a perfect field. The authors conctruct a tensor triangulated category of mixed motives over the truncated polynomial ring \(k[t]/(t^{m+1})\). This category is expected by the authors to be an appriopriate extension of the category of mixed motives to the simplest types of non-reduced rings. The motivic cohomology given by the Ext-groups in this category are given by Bloch's higher Chow groups and the additive higher Chow groups. The main technical result of the paper is the moving lemma for additive higher Chow groups and its refinements. The complete construction of such a category would allow one to construct the motivic cohomology that compute the \(K\)-theory of vector bundles on singular varieties. The authors study the particular case of this problem concerning singular varieties which are the infinitesimal deformations of smooth varieties.
reviewed by: Piotr Krasoń
description: scientific article; zbMATH DE number 6051264