Stable functors of derived equivalences and Gorenstein projective modules
Stable functors of derived equivalences and Gorenstein projective modules
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导出等价的稳定函子和 Gorenstein 射影模
DOI：
10.1002/mana.201600179
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发表时间：
2017
影响因子：
1
通讯作者：
Pan Shengyong
中科院分区：
文献类型：
--
作者：
Hu Wei;Pan Shengyong
从具有足够投射对象的阿贝尔范畴的有界导范畴之间的某些三角函子（称为非负函子）出发，引入了它们的稳定函子，即阿贝尔范畴的稳定范畴之间的某些加性函子.该建筑概括了胡和习以前的工作。证明了非负函子的稳定函子具有良好的正合性，并且与函子的合成相容。这使我们能够方便地比较由稳定函子链接的对象的同调性质。特别是，我们证明了两个任意环之间的导出等价的稳定函子提供了显式的Gorenstein投射模的稳定类别之间的三角等价。这推广了Y.加藤我们的结果也可以用来提供一些已知的同调代数结果的更短的证明。
From certain triangle functors, called nonnegative functors, between the bounded derived categories of abelian categories with enough projective objects, we introduce their stable functors which are certain additive functors between the stable categories of the abelian categories. The construction generalizes a previous work by Hu and Xi. We show that the stable functors of nonnegative functors have nice exactness property and are compatible with composition of functors. This allows us to compare conveniently the homological properties of objects linked by the stable functors. In particular, we prove that the stable functor of a derived equivalence between two arbitrary rings provides an explicit triangle equivalence between the stable categories of Gorenstein projective modules. This generalizes a result of Y. Kato. Our results can also be applied to provide shorter proofs of some known results on homological conjectures.