Motivic decomposability of generalized Severi-Brauer varieties

作者：Zhykhovich Maksim^*

来源：Comptes Rendus Mathematique, 2010, 348(17-18): 989-992.

DOI：10.1016/j.crma.2010.07.022

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 >= 1. 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.

• 出版日期2010-9