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Original Articles

Recollements of Singularity Categories and Monomorphism Categories

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Pages 2443-2456 | Received 30 Jan 2013, Published online: 17 Apr 2015

REFERENCES

  • Auslander , M. , Reiten , I. ( 1991 ). Applications of contravariantly finite subcategories . Adv. Math. 86 : 111 โ€“ 152 .
  • Beilinson , A. , Bernstein , J. , Deligne , P. ( 1982 ). Faisceaux pervers. Astรฉrisque 100 .
  • Brenner , S. , Butler , M. ( 1980 ). Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors . In: Dlab , V. , Gabriel , P. , eds. Representation Theory II (Ottawa, 1979) . Lecture Notes in Math. , Vol. 832. Berlin : Springer-Verlag , pp. 103 โ€“ 169 .
  • Buchweitz , R. ( 1987 ). Maximal Cohen-Macaulay modules and Tate cohomology over Gorenstein Rings, Unpublished Manuscript, Availble at: Http://hdl.handle.net/1807/16682 .
  • Chen , J.-M. , Lin , Y.-N. , Ruan , S.-Q. ( 2014 ). Tilting objects in the stable category of vector bundles on the weighted projective line of type (2, 2, 2, 2; ฮป) . J. Algebra 397 : 570 โ€“ 588 .
  • Chen , J.-M. , Lin , Y.-N. , Liu , P. , Ruan , S.-Q. Classification of tilting objects on a weighted projective line of type (2, 2, 2, 2; ฮป). preprint, arXiv: 1303.1323.
  • Chen , Q.-H. , Lin , Y.-N. ( 2003 ). Recollements of extension of algebras . Sci. in China (Series A) 46 ( 4 ): 530 โ€“ 537 .
  • Chen , X.-W. ( 2009 ). Singularity categories, Schur functors and triangular matrix rings . Algebr. Represent. Theor. 12 : 181 โ€“ 191 .
  • Chen , X.-W. ( 2011 ). The stable monomorphism category of a Frobenius category . Math. Res. Lett. 18 ( 1 ): 127 โ€“ 139 .
  • Chen , X.-W. ( 2012 ). A recollement of vector bundles . Bulletin of the London Math. Soc. 44 : 271 โ€“ 284 .
  • Cline , E. , Parshall , B. , Scott , L. ( 1986 ). Algebraic stratification in representation categories . J. Algebra 104 : 397 โ€“ 409 .
  • Geigel , W. , Lenzing , H. ( 1987 ). A class of weighted projective curves arising in representation theory of finite dimensional algebras . In: Greuel , G.-M. , Trautmann , G. , eds. Singularities, Representations of Algebras, and Vector Bundles (Lambrecht, 1985) . Lecture Notes in Math. , Vol. 1273. Berlin : Springer-Verlag , pp. 265 โ€“ 297 .
  • Happel , D. ( 1991 ). On Gorenstein algebras . In: Progress in Math. . Vol. 95 . Basel : Birkhรคuser Verlag, pp . 389 โ€“ 404 .
  • Happel , D. ( 1988 ). Triangulated Categories in the Representation Theory of Finite-dimensional Algebras . London Math. Soc. Lecture Note Ser. , Vol. 119. Cambridge : Cambridge University Press .
  • Iyama , O. , Kato , K. , Miyachi , J. ( 2011 ). Recollement of homotopy categories and Cohen-Macaulay modules . J. K-Theory 8 ( 3 ): 507 โ€“ 542 .
  • Jรธrgensen , P. ( 2006 ). Recollement for differential graded algebras . J. Algebra 299 : 589 โ€“ 601 .
  • Kashiwara , M. , Schapira , P. ( 1990 ). Sheaves on Manifolds . Grundlehren , Vol. 292. Berlin Heidelberg : Springer-Verlag .
  • Koenig , S. ( 1991 ). Tilting complexes, perpendicular categories and recollements of derived module categories of rings . J. Pure Appl. Algebra 73 : 211 โ€“ 232 .
  • Krause , H. ( 2010 ). Localization theory for triangulated categories . In: Triangulated Categories . London Math. Soc. Lecture Note Ser., Vol. 375 . Cambridge : Cambridge Univ. Press , pp. 161C235 .
  • Kussin , D. , Lenzing , H. , Meltzer , H. ( 2013 ). Nilpotent operators and weighted projective lines . J. Reine Angew. Math. 685 : 33 โ€“ 71 .
  • Kussin , D. , Lenzing , H. , Meltzer , H. ( 2013 ). Triangle singularities, ADE-chains, and weighted projective lines . Advances in Mathematics 237 : 194 โ€“ 251 .
  • Lin , Z.-Q. ( 2010 ). Recollement of quotient categories . Chinese Ann. of Math, Series A 31 ( 5 ): 525 โ€“ 530 .
  • Orlov , D. (2004). Triangulated categories of singularities and D-branes in Landau-Ginzburg models. Proc. Steklv Inst. Math. 246(3):227โ€“248.
  • Parshall , B. , Scott , L. ( 1988 ). Derived categories, quasi-hereditary algebras, and algebraic groups . In: Proceedings of the Ottawa-Moosonee Workshop in Algebra (1987). Carleton Univ., Ottawa, ON .
  • Ringel , C. M. ( 1984 ). Tame Algebras and Integral Quadratic Forms . Lecture Notes in Math. , Vol. 1099. Berlin : Springel-Verlag .
  • Ringel , C. M. , Schmidmeier , M. ( 2006 ). Submodule categories of wild representation type . J. Pure Appl. Algebra 205 : 412 โ€“ 422 .
  • Ringel , C. M. , Schmidmeier , M. ( 2008 ). The Auslander-Reiten translation in submodule category . Trans. Amer. Math. Soc. 360 : 691 โ€“ 716 .
  • Ringel , C. M. , Schmidmeier , M. ( 2008 ). Invariant subspaces of nilpotent linear operators . J. Reine Angew. Math. 614 : 1 โ€“ 52 .
  • Verdier , J. ( 1977 ). Catรฉgories dรฉrivรฉes . In: SGA 4 1/2 . Lecture Notes in Math., Vol. 569 . Berlin : Springer-Verlag .
  • Xiong , B.-L. , Zhang , P. ( 2012 ). Gorenstein-projective modules over triangular matrix Artin algebras . J. Algebra Appl. 11 : 1250066 .
  • Zhang , P. ( 2011 ). Monomorphism categories, cotilting theory, and Gorenstein-projective modules . J. Algebra 339 : 181 โ€“ 202 .
  • Zhang , P. ( 2013 ). Gorenstein-projective modules and symmetric recollements . J. Algebra 388 : 65 โ€“ 80 .
  • Communicated by D. Zacharia.

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