Geodesic
Stable Homotopy Theory of Simplicial Presheaves
Canadian journal of mathematics, Tome 39 (1987) no. 3, pp. 733-747

Voir la notice de l'article provenant de la source Cambridge University Press

Let C be an arbitrary Grothendieck site. The purpose of this note is to show that, with the closed model structure on the category S Pre(C) of simplicial presheaves in hand, it is a relatively simple matter to show that the category S Pre(C)stab of presheaves of spectra (of simplicial sets) satisfies the axioms for a closed model category, giving rise to a stable homotopy theory for simplicial presheaves. The proof is modelled on the corresponding result for simplicial sets which is given in [1], and makes direct use of their Theorem A.7.This result gives a precise description of the associated stable homotopy category Ho(S Pre(C))stab, according to well known results of Quillen [6]. One will recall, however, that it is preferable to have several different descriptions of the stable homotopy category, for the construction of smash products and the like. 
Jardine, J. F. Stable Homotopy Theory of Simplicial Presheaves. Canadian journal of mathematics, Tome 39 (1987) no. 3, pp. 733-747. doi: 10.4153/CJM-1987-035-8
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