### Hypercohomology spectra and Thomason's descent theorem, by Stephen A. Mitchell

This is an expository paper on Thomason's etale descent theorem for
Bott-periodic algebraic K-theory. It is mainly concerned with the proof of
the theorem, and the machinery that goes into the proof. It includes an
exposition of Jardine's closed model category structure on presheaves of
spectra. Much background material is provided on Grothendieck sites, sheaf
cohomology, etc. The paper is arranged so that readers who are not familiar
with schemes or etale cohomology can still read the first and last
chapters, which deal with Thomason's theorem for fields.

This paper will appear in the proceedings of the 1996 Great Lakes K-theory
conference.

Section 5.3 of the
original version
of this paper was mostly nonsense as
written. I thank Bruno Kahn for pointing this out. This edition corrects
5.3.

Stephen A. Mitchell <mitchell@math.washington.edu>