Models for singularity categories
Models for singularity categories
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DOI：
10.1016/j.aim.2013.11.016
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发表时间：
2012-05
期刊：
影响因子：
--
通讯作者：
Hanno Becker
中科院分区：
文献类型：
--
作者：
Hanno Becker
在本文中，我们为微分分级环上的模块的奇点类别构建了各种模型。主要技术是阿贝尔模型结构、扭曲对和可解构类之间的连接，我们的构造基于关于阿贝尔模型结构的本地化和传递的更一般的结果。我们指出了如何以分类方式获得三角类别的重新整理模型，并详细讨论了克劳斯的重新整理 K ac (Inj (R))→ K (Inj (R))→ D (R)。在弯曲混合 Z 梯度复形的特殊情况下，我们表明我们的奇异模型之一是 Quillen 等价于 Positselski 的矩阵分解同伦范畴的逆导出模型。
In this article we construct various models for singularity categories of modules over differential graded rings. The main technique is the connection between abelian model structures, cotorsion pairs and deconstructible classes, and our constructions are based on more general results about localization and transfer of abelian model structures. We indicate how recollements of triangulated categories can be obtained model categorically, discussing in detail Krauseʼs recollement K ac (Inj (R))→ K (Inj (R))→ D (R). In the special case of curved mixed Z-graded complexes, we show that one of our singular models is Quillen equivalent to Positselskiʼs contraderived model for the homotopy category of matrix factorizations.