Change of rings and singularity categories
Change of rings and singularity categories
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DOI：
10.1016/j.aim.2019.04.029
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发表时间：
2018-01
影响因子：
1.7
通讯作者：
Steffen Oppermann;Chrysostomos Psaroudakis;Torkil Stai
中科院分区：
文献类型：
--
作者：
Steffen Oppermann;Chrysostomos Psaroudakis;Torkil Stai
研究了Gorenstein投射模沿着环的一个态射的奇异范畴和稳定范畴的行为。解决这个问题的自然背景是通过环的变化，即模范畴之间的经典伴随三元组。特别是，我们确定环的变化，以诱导函子之间的两个奇异类别或两个稳定类别的Gorenstein投射模的条件。此外，我们在Krause [30]意义下的“大奇点范畴”水平上研究了这个问题。沿着的方式，我们建立了一个明确的结构，一个右伴随函子之间的某些同伦范畴。这是通过在三角范畴中引入0-余紧对象的概念并证明Bousfield局部化引理的对偶版本来实现的。我们提供的应用程序和例子说明我们的主要结果。
We investigate the behavior of singularity categories and stable categories of Gorenstein projective modules along a morphism of rings. The natural context to approach the problem is via change of rings, that is, the classical adjoint triple between the module categories. In particular, we identify conditions on the change of rings to induce functors between the two singularity categories or the two stable categories of Gorenstein projective modules. Moreover, we study this problem at the level of ‘big singularity categories’ in the sense of Krause [30]. Along the way we establish an explicit construction of a right adjoint functor between certain homotopy categories. This is achieved by introducing the notion of 0-cocompact objects in triangulated categories and proving a dual version of Bousfield's localization lemma. We provide applications and examples illustrating our main results.