We construct an ^-adic formalism of derived categories for algebraic
stacks. Over finite fields we generalize the theory of mixed complexes to
a theory of so called convergent complexes. This leads to a proof of the
Lefschetz Trace Formula for the Frobenius.
Received by the editor July 25, 1999 and in revised form June 5, 2000.
1991 Mathematics Subject Classification. 14D20, 18Gxx.
Key words and phrases, stacks, derived categories, Lefschetz trace formula.
Supported in part by a grant from the National Science Foundation.