K-Theory of Azumaya Algebras over Schemes, by R. Hazrat and R. T. Hoobler

Let X be a connected, noetherian scheme and A be a sheaf of Azumaya algebras on X which is a locally free O_X-module of rank a. We show that the kernel and cokernel of K_i(X) ----> K_i(A) are torsion groups with exponent a^m for some m and any i \geq 0, when X is regular or X is of dimension d with an ample sheaf (in this case m \leq d+1). As a consequence, K_i(X,Z/m) is isomorphic to K_i(A,Z/m), for any m relatively prime to a.

R. Hazrat <r.hazrat@qub.ac.uk>
R. T. Hoobler <rthccc@gmail.com>