Dimensions of triangulated categories with respect to subcategories
Dimensions of triangulated categories with respect to subcategories
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DOI：
10.1016/j.jalgebra.2013.09.035
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发表时间：
2012-04
期刊：
影响因子：
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通讯作者：
T. Aihara;Tokuji Araya;O. Iyama;Ryo Takahashi;Michio Yoshiwaki
中科院分区：
文献类型：
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作者：
T. Aihara;Tokuji Araya;O. Iyama;Ryo Takahashi;Michio Yoshiwaki
本文引入了三角范畴关于固定满子范畴的维数的概念。对于阿贝尔范畴的有界导范畴，给出了关于反变有限子范畴和可分解子范畴的维数上界。我们的方法不仅恢复了Rouquier意义下导出范畴维数的一些已知结果，而且适用于各种交换和非交换Noether环。
This paper introduces a concept of dimension of a triangulated category with respect to a fixed full subcategory. For the bounded derived category of an abelian category, upper bounds of the dimension with respect to a contravariantly finite subcategory and a resolving subcategory are given. Our methods not only recover some known results on the dimensions of derived categories in the sense of Rouquier, but also apply to various commutative and non-commutative noetherian rings.