Jardine, J. F. Stable homotopy theory of simplicial presheaves. (English) Zbl 0645.18006 Can. J. Math. 39, No. 3, 733-747 (1987). By using appropriate (and natural) definitions of fibration, cofibration, and weak equivalence, the author proves that the category of presheaves of spectra of simplicial sets is a proper closed simplicial model category in the sense of Quillen. For the etale site of a “decent” scheme, the etale K-groups of Dwyer and Friedlander can then be captured as homotopy groups for this model structure. Reviewer: D.H.van Osdol Cited in 3 ReviewsCited in 20 Documents MSC: 18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) Keywords:category of presheaves of spectra of simplicial sets; closed simplicial model category; etale K-groups; homotopy groups PDF BibTeX XML Cite \textit{J. F. Jardine}, Can. J. Math. 39, No. 3, 733--747 (1987; Zbl 0645.18006) Full Text: DOI