纯奇点范畴中的Buchweitz定理
Buchweitz Theorem in Pure Singularity Category
我们定义纯奇点范畴Dpsgb(R)为有界纯导出范畴Dpurb(R)与纯投射模构成的有界同伦范畴Kb(PP)的Verdier商,得到了纯奇点范畴Dpsgb(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Dpsgb(R)≈Dpsgb(S)的充分条件,这里R和S都是环.
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.
纯导出范畴 / 稳定范畴 / 纯奇点范畴 {{custom_keyword}} /
pure derived category / stable category / pure singularity category {{custom_keyword}} /
[1] Asadollahi J., Hafezi R., Vahed R., Gorenstein derived equivalences and their invariants, J. Pure Appl. Algebra, 2014, 218(5):888-903.
[2] Bao Y. H., Du X. N., Zhao Z. B., Gorenstein singularity categories, J. Algebra, 2015, 428:122-137.
[3] Buchweitz R. O., Matrix Cohen-Macaulay modules and Tate cohomology over Gorenstein rings, Hamburg, 1987, 155 pp., unpublished manuscript.
[4] Chen W. J., Liu Z. K., Yang X. Y., Singularity categories with respect to Ding projective modules, Acta Math. Sinica, 2017, 33:793-806.
[5] Chen X. W., Relative singularity categories and Gorenstein projective modules, Math. Nachr, 2011, 284:199-212.
[6] Enochs E. E., Jenda O. M. G., López-Ramos J. A., Covers and envelopes by V -Gorenstein modules, Comm. Algebra, 2005, 33:4705-4717.
[7] Huang Z. Y., Proper resolutions and Gorenstein categories, J. Algebra, 2013, 393:142-169.
[8] Kong F., Zhang P., From CM-finite to CM-free, J. Pure Appl. Algebra, 2016, 220:782-801.
[9] Li H. H., Huang Z. Y., Relative singularity categories, J. Pure Appl. Algebra, 2015, 219:4090-4104.
[10] Orlov D., Triangulated categories of singularities and D-branes in Landau-Ginzburg models, Proc. Steklov Inst. Math., 2004, 246:227-248.
[11] Rickard J., Derived categories and stable equivalence, J. Pure Appl. Algebra, 1989, 61:303-317.
[12] Sather-Wagstaff S., Sharif T., White D., Stability of Gorenstein categories, J. Lond. Math. Soc., 2008, 77:481-502.
[13] Verdier J. L., Des Catégories Dérivées Abéliennes, Asterisque, 1996, 239:xii+253 pp.
[14] Zheng Y. F., Huang Z. Y., On pure derived categories, J. Algebra, 2016, 454:252-272.
[15] Zhang P., Triangulated Category and Derived Category (in Chinese), Science Press, Beijing, 2015.
[16] Zhu S. J., Left Homotopy Theory and Buchweitz's Theorem, Master Thesis at Shanghai Jiaotong Universty, Shanghai, 2011.
国家自然科学基金资助项目(11761060)
/
〈 | 〉 |