Uniqueness of enhancement for triangulated categories
Uniqueness of enhancement for triangulated categories
复制标题
三角类别增强的唯一性
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Dmitri Orlov
中科院分区：
文献类型：
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作者：
V. Lunts;Dmitri Orlov
本文包含关于三角类别 DG 增强的唯一性的一般结果。因此，我们获得了准相干滑轮的无界范畴、完美复形的三角剖分范畴以及准射影格式上的相干滑轮的有界派生范畴的唯一性。如果一个方案是射影的，那么我们还证明了完美复合体的三角剖分范畴和相干滑轮的有界派生范畴的强唯一性。这些结果直接意味着来自相干滑轮的有界派生类别和射影方案上完美复形的三角化类别的完全忠实函子可以由乘积上的对象表示。
The paper contains general results on the uniqueness of a DG enhancement for trian- gulated categories. As a consequence we obtain such uniqueness for the unbounded categories of quasi-coherent sheaves, for the triangulated categories of perfect complexes, and for the bounded de- rived categories of coherent sheaves on quasi-projective schemes. If a scheme is projective then we also prove a strong uniqueness for the triangulated category of perfect complexes and for the bounded de- rived categories of coherent sheaves. These results directly imply that fully faithful functors from the bounded derived categories of coherent sheaves and the triangulated categories of perfect complexes on projective schemes can be represented by objects on the product.