相对奇点范畴和相对亏范畴

发布时间：2018-05-14 10:33

本文选题：范畴局部化 + 左乘法系　；参考：《华东师范大学》2015年硕士论文

【摘要】：本文研究Abel范畴的可容许子范畴的相对奇点范畴与相对亏范畴。首先,本文回顾了范畴的局部化、乘法系与饱和乘法系的概念,特别地,我们指出了一些结论对于左乘法系也是成立的。其次,我们研究了一个Artin代数的有限生成左模范畴的奇点范畴与它的一个左正交子范畴的加法生成子的自同态环的奇点范畴之间的关系,这给出了章璞教授近期的一个结果的范畴化解释。最后,给定一个Abel范畴,我们定义了一个可容许子范畴的相对亏范畴,并且在比较弱的条件下证明了一个可容许子范畴的相对亏范畴等价于它的Gorenstein范畴的相对奇点范畴,这推广了孔繁-章璞与鲍炎红-杜先能-赵志兵分别独立证明的结果。
[Abstract]:In this paper, we study the relative singularities and relative deficient categories of admissible subcategories of Abel categories. First of all, we review the concepts of category localization, multiplication system and saturated multiplication system. In particular, we point out that some conclusions are also true for the left multiplication system. Secondly, we study the relations between the singularity category of the finitely generated left module category of a Artin algebra and the singularity category of the endomorphism ring of an additive generator of its left orthogonal subcategory. This gives a categorization explanation of Professor Zhang Pu's recent results. Finally, given a Abel category, we define the relative deficient category of an admissible subcategory, and prove that the relative deficient category of an admissible subcategory is equivalent to the relative singularity category of its Gorenstein category under relatively weak conditions. This extends the results that Kong Fan-Zhang Pu and Bao Yanhong-du Xianeng-Zhao Zhibing independently prove respectively.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O154.1

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