Index Reduction Formulas for Twisted Flag Varieties, I, by A. S. Merkurjev, I. A. Panin, and A. R. Wadsworth

We prove a general formula for computing the Schur index of A tensor F(X), where A is a central simple algebra over a field F and F(X) is the function field of a twisted flag variety X; that is, X is a projective variety over F such that there is an algebraic group action on X by some adjoint semisimple group G, where the action becomes transitive on passage to the separable closure of F. The formula depends on the calculation of K_0(X;A) made by the second author. When G is a classical simple group of inner type, the corresponding varieties X are classified, and explicit concise index reduction formulas are given for each X.

This paper has appeared in the journal K-theory, 10 (1996), 517-596, and hence the dvi file has been removed.


A. S. Merkurjev <merkurev@pdmi.ras.ru>
I. A. Panin <panin@pdmi.ras.ru>
A. R. Wadsworth <arwadsworth@ucsd.edu>