参考文献:1. Auslander M., Ding S., Solberg ?.: Liftings and weak liftings of modules. J. Algebra 156, 273-17 (1993) CrossRef 2. Auslander M., Reiten I.: On a generalized version of the Nakayama conjecture. Proc. AMS 52, 69-4 (1975) CrossRef 3. Auslander M., Reiten I., Smal? S.O.: Representation Theory of Artin Algebras. Cambridge University Press, London (1995) CrossRef 4. Auslander M., Reiten I.: Applications of contravariantly finite subcategories. Adv. Math. 86(1), 111-52 (1991) CrossRef 5. Christensen L.W., Holm H.: Algebras that satisfy Auslander’s condition on vanishing of cohomology. Math. Z. 265, 21-0 (2010) CrossRef 6. Happel D.: Reduction techniques for homological conjectures. Tsukuba J. Math. 17(1), 115-30 (1993) 7. Happel D.: Triangulated Categories in the Representation Theory of Finite Dimensional Algebras. London Mathematical Society Lecture Note Series, vol. 119. Cambridge University Press, Cambridge (1988) CrossRef 8. Hoshino M.: Modules without self-extensions and Nakayama’s conjecture. Arch. Math. 43, 494-00 (1984) CrossRef 9. Huneke C., Leuschke G.J.: On a conjecture of Auslander and Reiten. J. Algebra 275, 781-90 (2004) CrossRef 10. Huneke C., Sega L.M., Vraciu A.N.: Vanishing of Ext and Tor over some Cohen-Macaulay local rings. Ill. J. Math. 48, 295-17 (2004) 11. Miyashita Y.: Tilting modules of finite projective dimension. Math. Z. 193, 113-46 (1986) CrossRef 12. Pan S., Xi C.: Finiteness of finitistic dimension is invariant under derived equivalences. J. Algebra 322, 21-4 (2009) CrossRef 13. Rickard J.: Morita theory for derived categories. J. Lond. Math. Soc. 39, 436-56 (1989) CrossRef 14. Wei J.: Tilting invariance of the Auslander-Reiten conjecture. Math. Res. Lett. 17(1), 171-76 (2010) 15. Wei J.: Auslander bounds and homological conjectures. Rev. Mat. Iberoamericana 27(3), 871-84 (2011) CrossRef 16. Wei J., Xi C.: A characterization of tilting pairs. J. Algebra 317, 376-91 (2007) CrossRef 17. Zimmermann Huisgen B.: The finitistic dimension conjectures—a tale of 3.5 decades. In: Facchini, A., Menini, C (eds) Abelian Groups and Modules, Proceedings of the Padova Conference 1994, Kluwer, Dordrecht (1995)
作者单位:Jiaqun Wei (1)
1. Institute of Mathematics, School of Mathematics Sciences, Nanjing Normal University, Nanjing, 210046, People’s Republic of China
ISSN:1432-1823
文摘
We studied the properties of tilting complexes and proved that derived equivalences preserve the validity of the Auslander–Reiten conjecture.