maksim.zhykhovich at gmail.com

Submission: 2009, Oct 26

Let F be an arbitrary field. Let p be a positive prime number and D a
central division F-algebra of degree p^n, with n>0.
We write SB(p^m,D) for the generalized Severi-Brauer variety of right ideals
in D of reduced dimension p^m for m=0,1, ... ,n-1.
We note by M(SB(p^m,D)) the Chow motive with coefficients in F_p of the
variety SB(p^m,D).
It was proven by Nikita Karpenko that this motive is indecomposable for any
prime p and m=0 and for p=2, m=1.
We prove decomposability of M(SB(p^m, D)) in all the other cases(p=2, 1

2000 Mathematics Subject Classification: 14M15; 14C25

Keywords and Phrases: Chow groups, motivic decomposition, Severi-Brauer varieties

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