Chow motives of twisted flag varieties
نویسندگان
چکیده
منابع مشابه
Chow motives of twisted flag varieties
Let G be an adjoint simple algebraic group of inner type. We express the Chow motive (with integral coefficients) of some anisotropic projective G-homogeneous varieties in terms of motives of simpler G-homogeneous varieties, namely, those that correspond to maximal parabolic subgroups of G. We decompose the motive of a generalized Severi-Brauer variety SB2(A), where A is a division algebra of d...
متن کاملChow Groups of Some Generically Twisted Flag Varieties
We classify the split simple affine algebraic groups G of types A and C over a field with the property that the Chow group of the quotient variety E/P is torsion-free, where P ⊂ G is a special parabolic subgroup (e.g., a Borel subgroup) and E is a generic G-torsor (over a field extension of the base field). Examples of G include the adjoint groups of type A. Examples of E/P include the Severi-B...
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Let G be a split semisimple algebraic group over a field k and let X be the flag variety (i.e., the variety of Borel subgroups) of G twisted by a generic G-torsor. We start a systematic study of the conjecture, raised in [8] in form of a question, that the canonical epimorphism of the Chow ring of X onto the associated graded ring of the topological filtration on the Grothendieck ring of X is a...
متن کاملGrothendieck Chow-motives of Severi-Brauer varieties
For any central simple algebra, the Grothendieck Chow-motive of the corresponding Severi-Brauer variety is decomposed in a direct sum where each summand is a twisted motive of the Severi-Brauer variety corresponding to the underlying division algebra. It leads to decompositions in other theories (for instance, of K-cohomologies) because of the universal property of the Chow-motives. In the seco...
متن کاملChow Ring of Generically Twisted Varieties of Complete Flags
Let G be a split simple affine algebraic group of type A or C over a field k, and let E be a standard generic G-torsor over a field extension of k. We compute the Chow ring of the variety of Borel subgroups of G (also called the variety of complete flags of G), twisted by E. In most cases, the answer contains a large finite torsion subgroup. The torsion-free cases have been treated in the prede...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2006
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x06002053