Geodesic
Decompositions of motives of generalized Severi-Brauer varieties
Documenta mathematica, Tome 17 (2012), pp. 151-165.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $p$ be a positive prime number and $X$ be a Severi-Brauer variety of a central division algebra $D$ of degree $p^n$, with $n\geq 1$. We describe all shifts of the motive of $X$ in the complete motivic decomposition of a variety $Y$, which splits over the function field of $X$ and satisfies the nilpotence principle. In particular, we prove the motivic decomposability of generalized Severi-Brauer varieties $X(p^m,D)$ of right ideals in $D$ of reduced dimension $p^m, m=0,1,ldots,n-1$, except the cases $p=2, m=1$ and $m=0 (for any prime p)$, where motivic indecomposability was proven by Nikita Karpenko.
Classification : 14L17, 14C25
Keywords: central simple algebras, generalized Severi-Brauer varieties, Chow groups and motives 
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     author = {Zhykhovich, Maksim},
     title = {Decompositions of motives of generalized {Severi-Brauer} varieties},
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     year = {2012},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a24/}
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Zhykhovich, Maksim. Decompositions of motives of generalized Severi-Brauer varieties. Documenta mathematica, Tome 17 (2012), pp. 151-165. http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a24/