Gorenstein导出范畴中的若干问题

发布时间：2018-03-26 19:42

本文选题：Gorenstein导出范畴　切入点：Gorenstein导出函子　出处：《西北民族大学》2017年硕士论文

【摘要】：由Grothendieck-Verdier在上个世纪60年代引入了导出范畴的概念,在代数表示论和代数几何等领域取得巨大成功.2010年高楠和章璞引入了 Gorenstein导出范畴并得到了 Gorenstein导出范畴的一些基本结论.而后高楠对Gorenstein导出范畴,奇点范畴,Gorenstein导出等价,三角粘合进行了一系列研究.伊朗学者Asadolahi也在Gorenstein导出范畴中得到了许多令人满意的结论.本文由三部分组成.第一部分主要介绍本文所需的三角范畴,Gorenste:in同调代数和表示论的一些基本结论.第二部分给出了 Gorenstein导出范畴的两个等价定义,并考虑了 Gorenstein导出函子,得到了 Gorenstein导出函子存在性的一个充分条件.第三部分给出了一些经典结论在Gorenstein导出范畴中的推广得到了几个结论首先得到了:定理3.1.9若三角函子θ:g((?)→D(?)(A)是稠密的,则(?)-dimA∞,其中(?)是A的一个反变有限子范畴此外还得到了有限维代数的有界Gorenstein导出范畴中Auslander-Rieten三角存在的充要条件,考虑了 CM有限代数的Gorenstein导出等价并给出了一个Gorenstein导出范畴的三角粘合.
[Abstract]:The concept of 60s by Grothendieck-Verdier in the last century introduced the derived category, in the representation theory of algebras and algebraic geometry and other fields have achieved great success in.2010 high Pu Nan and chapter introduced Gorenstein derived category and some basic conclusions are obtained. Then Gorenstein derived category of Gao Nan Gorenstein derived category, singularity categories, Gorenstein derived equivalence, triangle the adhesive has carried out a series of research. Iran scholar Asadolahi has also been a lot of satisfactory results in the Gorenstein derived category. This paper consists of three parts. The first part mainly introduces the triangulated category required, Gorenste:in said some basic conclusions and homological algebra theory. The second part presents two equivalent definitions of Gorenstein derived categories and, considering the Gorenstein derived functor, and obtain a sufficient condition for the existence of Gorenstein derived functor. The third part gives the extension of some classical conclusions in Gorenstein derived category in the first several conclusions obtained: theorem 3.1.9 if the functor delta theta: G ((?), D (?) (A) is dense, then (?) -dimA 2, which (? A) is a counter variable the sub category also has finite dimensional algebras have necessary and sufficient conditions for the existence of Auslander-Rieten triangle Gorenstein derived category in the considered CM finite algebra Gorenstein derived equivalence and gives a triangular Gorenstein derived category of bonding.

【学位授予单位】：西北民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O154.1

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