Triangulated Categories: Derived categories and Grothendieck duality
Triangulated Categories: Derived categories and Grothendieck duality
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三角范畴：派生范畴和格洛腾迪克对偶性
DOI：
10.1017/cbo9781139107075.007
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发表时间：
2010
影响因子：
0.6
通讯作者：
A. Neeman
中科院分区：
文献类型：
--
作者：
A. Neeman
我们研究二元复合体。不寻常的特征是我们不假设它们具有有界内射分辨；我们证明了这个理论在没有有界性假设的情况下也能很好地工作。在此过程中，我们证明了一些关于Grothendieck对偶的新结果；其中一个更引人注目的是，在f: X−→Y的相对温和的假设下，函子f ！： D(Qcoh/Y)−→D（Qcoh/X）将假相干配合物转化为假相干配合物。我们方法中最大的创新是我们系统地使用D类（Qcoh/X）的产品；旧的治疗方法从来没有冒险超越副产品。在附录中，我们证明了如果T是[19]意义上的稳定同伦范畴，其中紧化对象与强对偶对象重合，则紧化对象也可以被表征为与它们张紧的对象是乘积。
We study dualizing complexes. The unusual feature is that we do not assume them to have bounded injective resolutions; we prove that the theory works just fine with no boundedness hypothesis. In the process we prove a number of new results about Grothendieck duality; one of the more striking is that, under relatively mild hypotheses on f : X −→ Y , the functor f ! : D(Qcoh/Y ) −→ D(Qcoh/X) takes pseudocoherent complexes to pseudocoherent complexes. The biggest innovation in our approach is that we systematically employ products in the category D(Qcoh/X); the older treatments never ventured beyond coproducts. In an appendix we include a proof that, if T is a stable homotopy category in the sense of [19] in which the compact objects coincide with the strongly dualizable objects, then the compact objects can also be characterized as those objects such that tensoring with them respects products.