Motivic decomposition of isotropic projective homogeneous varieties
type: Item
instance of: scholarly article
title: Motivic decomposition of isotropic projective homogeneous varieties
zbMATH Open document ID: 1086.14041
DOI: 10.1215/S0012-7094-04-12614-4
author: V. Chernousov
author: Stefan G. Gille
author: Alexander Merkurjev
published in: Duke Mathematical Journal
publication date: 2005-03-18T00:00:00Z
review text: The authors consider isotropic projective homogeneous varieties of arbitrary semisimple group over a field \(k\) and prove that the motive of such a variety is isomorphic to a direct sum of twisted motives of simpler projective homogeneous varieties. It is proved that all the information about such a decomposition is encoded in the root system of the group. To illustrate this, the authors work out the (essentially combinatorial) details for projective spaces, isotropic quadrics, and a homogeneous variety for the group of type \(E_6\). A new proof of Rost's decomposition theorem [\textit{M. Rost}, ``The motive of Pfister form'', Preprint (1998), \url{http//www.mathematik.uni-bielefeld.de/~rost/motive.html}] is given. As an application, the authors generalize Rost's nilpotence theorem to the case of arbitrary projective homogeneous varieties.
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 14F42
zbMATH DE Number: 2147027
zbMATH Keywords: Chow motive
zbMATH Keywords: homogeneous variety
zbMATH Keywords: semisimple algebraic group
reviewed by: Vladimir L. Popov
MaRDI profile type: Publication
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full work available at URL: s0012-7094-04-12614-4
OpenAlex ID: W2021893391
description: scientific article; zbMATH DE number 2147027