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arXiv · 1110.1023

Decompositions of motives of generalized Severi-Brauer varieties

Maksim Zhykhovich
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Abstract

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>0. 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,...,n-1, except the cases p=2, m=1 and m=0 (for any prime p), where motivic indecomposability was proven by Nikita Karpenko.

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Maksim Zhykhovich. 2012-04-06. Decompositions of motives of generalized Severi-Brauer varieties. https://arxiv.org/abs/1110.1023

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