Kirill Zainoulline: Motivic Decomposition of a generalized Severi-Brauer variety

Submission: 2006, Jan 27

Let $A$ and $B$ be two central simple algebras of a prime degree $n$ over a field $F$ generating the same subgroup in the Brauer group $Br(F)$. We show that the Chow motive of a Severi-Brauer variety $SB(A)$ is a direct summand of the motive of a generalized Severi-Brauer variety $SB_d(B)$ if and only if $[A]=\pm d[B]$ in the Brauer group $Br(F)$. The proof uses methods of Schubert calculus and combinatorial properties of Young tableaux, e.g., the Robinson-Schensted correspondence.

2000 Mathematics Subject Classification: 14C15; 14M15

Keywords and Phrases: Chow motive, Severi-Brauer variety, Grassmannian, Robinson-Schensted correspondence

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