Stable Homotopy Theory of Simplicial Presheaves
Stable Homotopy Theory of Simplicial Presheaves
复制标题
单纯预滑稳定同伦理论
DOI：
10.4153/cjm-1987-035-8
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
John F. Jardine
中科院分区：
文献类型：
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作者：
John F. Jardine
设C是任意的Grothendieck站点。本文的目的是证明，有了单纯预层范畴S Pre（C）上的闭模型结构，证明谱的（单纯集的）预层范畴S Pre（C）刺满足闭模型范畴的公理是一件相对简单的事情，从而产生了单纯预层的稳定同伦理论。本文的证明仿照了文[1]中关于单纯集的相应结果，并直接利用了文[1]中的定理A.7。根据Quillen [6]的著名结果，该结果给出了相关稳定同伦范畴Ho（S Pre（C））stab的精确描述.然而，我们会记得，为了构造smash积等，最好有几种不同的稳定同伦范畴的描述。
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.