Torsion Pairs in Stable Categories

REFERENCES

• Auslander , M. , Bridger , M. ( 1969 ). Stable module theory. Memoirs of the American Mathematical Society, No. 94. American Mathematical Society, Providence, Rhode Island, USA .
   Google Scholar
• Assem , I. , Beligiannis , A. , Marmaridis , N. ( 1998 ). Right triangulated categories with right semi-equivalences. Canandian Mathematical Society Conference Proceeding 24: 17–37 .
   Google Scholar
• Auslander , M. , Reiten , I. ( 1991 ). Applications of contravariantly finite subcategories . Advances in Mathematics 86 ( 1 ): 111 – 152 .
   Web of Science ®Google Scholar
• Assem , I. , Simson , D. , Skowronski , A. ( 2006 ). Elements of the Representation Theory of Associative Algebras . In : Volume 1: Techniques of Representation Theory. London Mathematical Society Student Text, 65. Cambridge: Cambridge University Press .
   Google Scholar
• Beligiannis , A. ( 2000 ). The homological theory of contravariantly finite subcategories: Auslander-Buchweitz contexts, Gorenstein categories and (co-)stabilization . Communications in Algebra 28 ( 10 ): 4547 – 4596 .
   Web of Science ®Google Scholar
• Beligiannis , A. ( 2001 ). Homotopy theory of modules and Gorenstein rings . Mathematica Scandinavica 89 ( 1 ): 5 – 45 .
   Web of Science ®Google Scholar
• Bondarko , M. V. ( 2010 ). Weight structures vs. t-structures; weight filtrations, spectral sequences, and complexes (for motives and in general) . K-Theory 6 ( 3 ): 387 – 504 .
   Google Scholar
• Beilinson , A. , Bernstein , J. , Deligne , P. ( 1982 ). Faisceaux pervers. In: Analyse et topologie sur les espaces singuliers . Astérisque 100 : 1 – 172 .
   Google Scholar
• Bondal , A. I. , Kapranov , M. M. ( 1990 ). Representable functors, Serre functors, and mutations . Mathematics of the USSR-Izvestiya 35 ( 3 ): 519 – 541 .
   Google Scholar
• Beligiannis , A. , Marmaridis , N. ( 1994 ). Left triangulated categories arising from contravariantly finite subcategories . Communications in Algebra 22 ( 12 ): 5021 – 5036 .
   Web of Science ®Google Scholar
• Buan , A. , Marsh , R. , Reineke , M. , Reiten , I. , Todorove , G. ( 2006 ). Tilting theory and cluster combinatorics . Advances in Mathematics 204 ( 2 ): 572 – 618 .
   Web of Science ®Google Scholar
• Beligiannis , A. , Reiten , I. ( 2007 ). Homological and homotopical aspects of torsion theories. Memoirs of the American Mathematical Society, 883:1–101 .
   Google Scholar
• Dickson , S. E. ( 1966 ). A torsion theory for abelian categories . Transactions of the American Mathematical Society 121 ( 1 ): 223 – 235 .
   Web of Science ®Google Scholar
• Iyama , O. , Yoshino , Y. ( 2008 ). Mutations in triangulated categories and rigid Cohen-Macaulay modules . Inventiones Mathematicae 172 ( 1 ): 117 – 168 .
   Web of Science ®Google Scholar
• Jøtrgensen , P. ( 2010 ). Quotients of cluster categories . Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140 ( 1 ): 65 – 81 .
   Google Scholar
• Keller , B. , Reiten , I. ( 2007 ). Cluster-tilted algebras are Gorenstein and stably Calabi-Yau . Advances in Mathematics 211 ( 1 ): 123 – 151 .
   Web of Science ®Google Scholar
• Neeman , A. ( 2001 ). Triangulated Categories . Princeton : Princeton University Press .
   Google Scholar
• Pauksztello , D. ( 2008 ). Compact corigid objects in triangulated categories and co-t-structures . Central European Journal of Mathematics 6 ( 1 ): 25 – 42 .
   Web of Science ®Google Scholar
• Quillen , D. ( 1967 ). Homotopical Algebra. Springer Lecture Notes in Math., Vol. 43 .
   Google Scholar
• Verdier , J. L. ( 1977 ). Catéegories dérivées, etat 0, SGA 4 1/2. Lecture Notes in Math., Vol. 569, pp. 262–311 .
   Google Scholar
• Communicated by A. Facchini.
   Google Scholar