论文标题
当地可观的Abelian DG类别的编码和矛盾类别
Coderived and contraderived categories of locally presentable abelian DG-categories
论文作者
论文摘要
Arxiv：2110.08237的名称作者提出的Abelian DG类别的概念将Abelian类别的概念和（弯曲的）DG模型统一在一个共同的框架中。在本文中，我们考虑了贝克尔的编码和矛盾类别。 Generalizing some constructions and results from the preceding papers by Becker arXiv:1205.4473 and by the present authors arXiv:2101.10797, we define the contraderived category of a locally presentable abelian DG-category $\mathbf B$ with enough projective objects and the coderived category of a Grothendieck abelian DG-category $\mathbf A$.我们构建了相关的Abelian模型类别结构，并表明由此产生的外来派生类别发电良好。然后，我们专门研究本地连贯的Grothendieck Abelian DG类别$ \ MATHBF a $，并证明其代码类别是由$ \ Mathbf a $的绝对派生类别的绝对派生类别所产生的，从而从第二名的作者的preprint Arint arxiv Arxiv Arxiv Arxiv：1416.125：14161.15.15.15.15.15.155。特别是，在DG环上的分级注射左DG模块的同型类别由具有左下的基础分级环由具有有限的基础分级模块的绝对派生类别的DG模块的绝对衍生类别生成。我们还描述了相干方案上准级矩阵因素化的编码类别的紧凑发电机。
The concept of an abelian DG-category, introduced by the first-named author in arXiv:2110.08237, unites the notions of abelian categories and (curved) DG-modules in a common framework. In this paper we consider coderived and contraderived categories in the sense of Becker. Generalizing some constructions and results from the preceding papers by Becker arXiv:1205.4473 and by the present authors arXiv:2101.10797, we define the contraderived category of a locally presentable abelian DG-category $\mathbf B$ with enough projective objects and the coderived category of a Grothendieck abelian DG-category $\mathbf A$. We construct the related abelian model category structures and show that the resulting exotic derived categories are well-generated. Then we specialize to the case of a locally coherent Grothendieck abelian DG-category $\mathbf A$, and prove that its coderived category is compactly generated by the absolute derived category of finitely presentable objects of $\mathbf A$, thus generalizing a result from the second-named author's preprint arXiv:1412.1615. In particular, the homotopy category of graded-injective left DG-modules over a DG-ring with a left coherent underlying graded ring is compactly generated by the absolute derived category of DG-modules with finitely presentable underlying graded modules. We also describe compact generators of the coderived categories of quasi-coherent matrix factorizations over coherent schemes.
