Summary: K-Theory 23: 251303, 2001.
c 2001 Kluwer Academic Publishers. Printed in the Netherlands.
Grothendieck Groups of Bundles on
Varieties over Finite Fields
and D. BURNS2
1Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.
2Department of Mathematics, King's College London, Strand, London WC2R 2LS, U.K.
(Received: July 2000)
Abstract. Let X be an irreducible, projective variety over a finite field, and let A be a sheaf of rings
on X. In this paper, we study Grothendieck groups of categories of vector bundles over certain types
of ringed spaces (X, A).
Mathematics Subject Classifications (2000): 11-XX, 19-XX, 14-XX, 13-XX.
Key words: Grothendieck groups, classgroups, sheaves of algebras, realisable classes, Witt vectors.
Let X be an irreducible, projective variety over a finite field k of characteristic p.
We write O, (or OX if we need to be more precise), for the structure sheaf of X. In