纯奇点范畴中的Buchweitz定理

曹天涯, 刘仲奎, 杨晓燕

数学学报 ›› 2019, Vol. 62 ›› Issue (4) : 553-560.

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数学学报 ›› 2019, Vol. 62 ›› Issue (4) : 553-560. DOI: 10.12386/A2019sxxb0052
论文

纯奇点范畴中的Buchweitz定理

    曹天涯, 刘仲奎, 杨晓燕
作者信息 +

Buchweitz Theorem in Pure Singularity Category

    Tian Ya CAO, Zhong Kui LIU, Xiao Yan YANG
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摘要

我们定义纯奇点范畴DpsgbR)为有界纯导出范畴DpurbR)与纯投射模构成的有界同伦范畴KbPP)的Verdier商,得到了纯奇点范畴DpsgbR)三角等价于相对纯投射模的Gorenstein范畴的稳定范畴GPP的一个充分必要条件.同时,还给出三角等价DpsgbR)≈DpsgbS)的充分条件,这里RS都是环.

Abstract

We define the pure singularity category Dpsgb(R) as the Verdier quotient of the bounded pure derived category Dpurb(R) by the triangulated subcategory Kb(PP) of the bounded homotopy category consisting of pure projective modules, a sufficient and necessary condition under which Dpsgb(R) is equivalent to the stable category of the Gorenstein category G (PP) of pure projective modules is given. Moreover, we give a sufficient condition for the triangle-equivalence Dpsgb(R)≈Dpsgb(S), where R and S are rings.

关键词

纯导出范畴 / 稳定范畴 / 纯奇点范畴

Key words

pure derived category / stable category / pure singularity category

引用本文

导出引用
曹天涯, 刘仲奎, 杨晓燕. 纯奇点范畴中的Buchweitz定理. 数学学报, 2019, 62(4): 553-560 https://doi.org/10.12386/A2019sxxb0052
Tian Ya CAO, Zhong Kui LIU, Xiao Yan YANG. Buchweitz Theorem in Pure Singularity Category. Acta Mathematica Sinica, Chinese Series, 2019, 62(4): 553-560 https://doi.org/10.12386/A2019sxxb0052

参考文献

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基金

国家自然科学基金资助项目(11761060)

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