Classification of upper motives of algebraic groups of inner type A_n

2011/01/24 by Charles De Clercq, De Clercq, Charles
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1101.4581

arxiv created 2011/01/24 · arxiv updated 2011/01/25

Abstract

Let A, A' be two central simple algebras over a field F and \mathbbF be a finite field of characteristic p. We prove that the upper indecomposable direct summands of the motives of two anisotropic varieties of flags of right ideals X(d₁,...,d_k;A) and X(d'₁,...,d'_s;A') with coefficients in \mathbbF are isomorphic if and only if the p-adic valuations of gcd(d₁,...,d_k) and gcd(d'₁,..,d'_s) are equal and the classes of the p-primary components A_p and A'_p of A and A' generate the same group in the Brauer group of F. This result leads to a surprising dichotomy between upper motives of absolutely simple adjoint algebraic groups of inner type A_n

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