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>