Decompositions of motives of generalized Severi-Brauer varieties
Maksim Zhykhovich
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Abstract
Let be a positive prime number and be a Severi-Brauer variety of a central division algebra of degree , with . We describe all shifts of the motive of in the complete motivic decomposition of a variety , which splits over the function field of and satisfies the nilpotence principle. In particular, we prove the motivic decomposability of generalized Severi-Brauer varieties of right ideals in of reduced dimension , except the cases and , where motivic indecomposability was proven by Nikita Karpenko.
Cite this article
Maksim Zhykhovich, Decompositions of motives of generalized Severi-Brauer varieties. Doc. Math. 17 (2012), pp. 151–165
DOI 10.4171/DM/364