Motivic decomposability of generalized Severi-Brauer varieties
type: Item
instance of: scholarly article
title: Motivic decomposability of generalized Severi-Brauer varieties
zbMATH Open document ID: 1233.14004
author: Maksim Zhykhovich
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2010-10-22T00:00:00Z
review text: Let \(F\) be a field, let \(p\) be a positive prime number and let \(D\) be a central division \(F\)-algebra of degree \(p^n\), with \(n\geq 1\). According to \textit{N. A. Karpenko} [St. Petersbg. Math. J. 7, No. 4, 649--661 (1996); translation from Algebra Anal. 7, No. 4, 196--213 (1995; Zbl 0866.14006); J. Reine Angew. Math. 677, 179--198 (2013; Zbl 1267.14009)], the Chow motive \(M(SB(p^m, D))\) with coefficients in \(\mathbb{F}_p\) of the generalized Severi--Brauer variety \(SB(p^m, D)\) of right ideals in \(D\) of reduced dimension \(p^m\) for \(m=0, 1,\dots, n-1\) is indecomposable for any \(p\) and \(m=0\) and for \(p=2\), \(m=1\). In this note decomposability of \(M(SB(p^m, D))\) in all the other cases is proved.
Mathematics Subject Classification ID: 14C15
Mathematics Subject Classification ID: 16K20
zbMATH DE Number: 5804394
zbMATH Keywords: central division algebra
zbMATH Keywords: Chow motive
reviewed by: Vladimir L. Popov
MaRDI profile type: Publication
full work available at URL: j.crma.2010.07.022
OpenAlex ID: W2091281051
cites work: Chow motives of twisted flag varieties
cites work: Motivic decomposition of projective homogeneous varieties and the Krull-Schmidt theorem
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DOI: 10.1016/J.CRMA.2010.07.022
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description: scientific article; zbMATH DE number 5804394