Upper motives of algebraic groups and incompressibility of Severi–Brauer varieties
Abstract
Let G be a semisimple affine algebraic group of inner type over a field F. We write đť”›G for the class of all finite direct products of projective G-homogeneous F-varieties. We determine the structure of the Chow motives with coefficients in a finite field of the varieties in đť”›G. More precisely, it is known that the motive of any variety in đť”›G decomposes (in a unique way) into a sum of indecomposable motives, and we describe the indecomposable summands which appear in the decompositions.
In the case where G is the group PGL A of automorphisms of a given central simple F-algebra A, for any variety in the class 𝔛G (which includes the generalized Severi–Brauer varieties of the algebra A) we determine its canonical dimension at any primep. In particular, we find out which varieties in 𝔛G are p-incompressible. If A is a division algebra of degree pn for some n ≧ 0, then the list of p-incompressible varieties includes the generalized Severi–Brauer variety X (pm;  A) of ideals of reduced dimension pm for m = 0, 1, …, n.
©[2013] by Walter de Gruyter Berlin Boston
Artikel in diesem Heft
- Essential dimension of algebraic tori
- K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space, II: A structure theorem for r(M) > 10
- Groups of positive weighted deficiency and their applications
- The Witt group of non-degenerate braided fusion categories
- Upper motives of algebraic groups and incompressibility of Severi–Brauer varieties
- Solution of a uniqueness problem in the discrete tomography of algebraic Delone sets
- Brauer group of moduli of principal bundles over a curve
Artikel in diesem Heft
- Essential dimension of algebraic tori
- K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space, II: A structure theorem for r(M) > 10
- Groups of positive weighted deficiency and their applications
- The Witt group of non-degenerate braided fusion categories
- Upper motives of algebraic groups and incompressibility of Severi–Brauer varieties
- Solution of a uniqueness problem in the discrete tomography of algebraic Delone sets
- Brauer group of moduli of principal bundles over a curve
