Variations on the Bloch-Ogus theorem.
-invariant of linear algebraic groups
Let be a semisimple linear algebraic group of inner type over a field , and let be a projective homogeneous -variety such that splits over the function field of . We introduce the -invariant of which characterizes the motivic behavior of , and generalizes the -invariant defined by A. Vishik in the context of quadratic forms. We use this -invariant to provide motivic decompositions of all generically split projective homogeneous -varieties, e.g. Severi-Brauer varieties, Pfister quadrics,...
Invariants, torsion indices and oriented cohomology of complete flags
Let be a split semisimple linear algebraic group over a field and let be a split maximal torus of . Let be an oriented cohomology (algebraic cobordism, connective -theory, Chow groups, Grothendieck’s , etc.) with formal group law . We construct a ring from and the characters of , that we call a formal group ring, and we define a characteristic ring morphism from this formal group ring to where is the variety of Borel subgroups of . Our main result says that when the torsion index...
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