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摘要翻译：
本文证明了对于一个拟紧半分离（非一定是noetherian）格式X，D(A_qc(X))上的拟相干束的导出范畴是Hovey、Palmieri和Strickland意义上的稳定同伦范畴，从而回答了Strickland提出的一个问题。此外，我们还证明了它的唯一性和代数性。我们还证明了对于一个noetherian半分离形式格式X，其导出的具有拟相干扭转同调的模束范畴D_qct(X)是一个稳定的同伦范畴。它是代数的，但如果形式图式不是通常图式，它就不是单一的，因此它的抽象性质与通常图式的派生范畴的抽象性质本质上不同。
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英文标题：
《The derived category of quasi-coherent sheaves and axiomatic stable
homotopy》
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作者：
Leovigildo Alonso, Ana Jeremias, Marta Perez, Maria J. Vale
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Algebraic Topology 代数拓扑
分类描述：Homotopy theory, homological algebra, algebraic treatments of manifolds
同伦理论，同调代数，流形的代数处理
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英文摘要：
We prove in this paper that for a quasi-compact and semi-separated (non necessarily noetherian) scheme X, the derived category of quasi-coherent sheaves over X, D(A_qc(X)), is a stable homotopy category in the sense of Hovey, Palmieri and Strickland, answering a question posed by Strickland. Moreover we show that it is unital and algebraic. We also prove that for a noetherian semi-separated formal scheme X, its derived category of sheaves of modules with quasi-coherent torsion homologies D_qct(X) is a stable homotopy category. It is algebraic but if the formal scheme is not a usual scheme, it is not unital, therefore its abstract nature differs essentially from that of the derived category of a usual scheme.
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PDF链接：
https://arxiv.org/pdf/0706.0493
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