2009/04/18 by Nikita A. Karpenko, Karpenko, Nikita A. · 2 citations
Mathematics · #14C25 #14L17 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG #msc:14C25 #msc:14L17
paper · pdf · doi:10.48550/arxiv.0904.2844
19 pages
openalex publication_date 2009/04/18 · arxiv created 2011/07/09 · arxiv updated 2011/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a semisimple affine algebraic group of inner type over a field F. We write C 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 C. More precisely, it is known that the motive of any variety in C 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 of automorphisms of a given central simple F-algebra A, for any variety in the class C (which includes the generalized Severi-Brauer varieties of the algebra A) we determine its canonical dimension at any prime p. In particular, we find out which varieties in C are p-incompressible. If A is a division algebra of degree pn for some n, 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.