环的弱整体维数和CM-自由性  

Weak global dimension and CM-freeness of rings

作　　者：汪军鹏 刘仲奎 张小向 Junpeng Wang;Zhongkui Liu;Xiaoxiang Zhang

机构地区：[1]西北师范大学数学与统计学院,兰州730070 [2]东南大学数学学院,南京210096

出　　处：《中国科学：数学》2022年第2期121-132,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11971388和11871145);西北师范大学青年教师科研能力提升计划(批准号:NWNU-LKQN2019-14);甘肃省高等学校创新项目(批准号:2020B-087)资助项目。

摘　　要：设环R的弱整体维数有限.本文证明R是强CM-自由的.作为应用,本文得到一些同伦范畴和相对导出范畴的三角等价和紧生成性.当R弱整体维数不超过1时,本文完全分类了这些等价范畴中的可定义子范畴,并说明这些等价的范畴在von Neumann正则环上满足Telescope猜想.同时将一个广义Grothendieck对偶型的三角等价成立的条件由R的左、右整体维数有限改进为仅右整体维数有限.Let R be a ring with finite weak global dimension.We prove that R is(strongly)CM-free.As applications,we obtain some triangulated equivalences between some compactly-generated homotopy categories and relative derived categories.We classify the definable categories of such equivalent triangulated categories when the weak global dimension of R is at most 1,and show that such equivalent triangulated categories satisfy Telescope conjecture when R is a von Neumann regular ring.We also improve the condition such that a triangulated equivalence about the extended Grothendieck duality holds from the finiteness of the left and right global dimension of R to only the finiteness of the right global dimension of R.

关 键 词：弱整体维数 (强)CM-自由性 紧生成性 可定义子范畴 Grothendieck对偶 

分 类 号：O153.3[理学—数学]