纯奇点范畴中的Buchweitz定理

我们定义纯奇点范畴Dpsg^b(R)为有界纯导出范畴Dpur^b(R)与纯投射模构成的有界同伦范畴K^b(PP)的Verdier商,得到了纯奇点范畴Dpsg^b(R)三角等价于相对纯投射模的Gorenstein范畴的稳定范畴g(PP)的一个充分必要条件.同时,还给出三角等价Dpsg^b(R)≌Dpsg^b(S)的充分条件,这里R和S都是环.

Buchweitz Theorem in Pure Singularity Category

We define the pure singularity category D_psg^b(R) as the Verdier quotient of the bounded pure derived category D_pur^b(R) by the triangulated subcategory K^b(PP) of the bounded homotopy category consisting of pure projective modules, a sufficient and necessary condition under which D_psg^b(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 D_psg^b(R)≈D_psg^b(S), where R and S are rings.