FUNCTION-FIELDS OF HOMOGENEOUS VARIETIES AND GALOIS COHOMOLOGY

Let V be a generalized flag variety over a field k. Then there exist f inite field extensions k(i) of k for 1 less than or equal to i less th an or equal to m, elements alpha(i) of the Brauer group of k(i) and a natural exact sequence +(m)(i=1) k(i) --> (N/k(boolean OR alpha i)(ki )) Ker(H-3 (k, Q/Z(2)) --> H-3 (k (V), Q/Z (2))) --> CH2 (V)(tors) --> 0 where the groups H-j (k, Q/Z(2)) are the Galois cohomology groups w ith coefficients in Q/Z twisted twice and CH2 (V) the Chow group of cy cles of codimension two module rational equivalence.