Frontiers of Mathematics in China >

2018 , Vol. 13 >Issue 4: 875 - 892

DOI: https://doi.org/10.1007/s11464-018-0712-1

RESEARCH ARTICLE

Torsion pairs in recollements of abelian categories

  • Xin MA 1 ,
  • Zhaoyong HUANG , 2
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  • 1. College of Science, Henan University of Engineering, Zhengzhou 451191, China
  • 2. Department of Mathematics, Nanjing University, Nanjing 210093, China

Received date: 11 Jan 2018

Accepted date: 11 Jul 2018

Published date: 14 Aug 2018

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

For a recollement (A ;ℬ; C ) of abelian categories, we show that torsion pairs in A and C can induce torsion pairs in ℬ; and the converse holds true under certain conditions.

Key words： Torsion pairs; recollements; abelian categories

Cite this article

Xin MA , Zhaoyong HUANG . Torsion pairs in recollements of abelian categories[J]. Frontiers of Mathematics in China, 2018 , 13(4) : 875 -892 . DOI: 10.1007/s11464-018-0712-1

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Auslander M, Reiten I, Smalø S O. Representation Theory of Artin Algebras. Cambridge Stud Adv Math, Vol 36. Cambridge: Cambridge Univ Press, 1997

2
Beĭlinson A A, Bernstein J, Deligne P. Faisceaux pervers, analysis and topology on singular spaces, I. Astérisque, 1982, 100: 5{171

3
Beligiannis A, Reiten I. Homological and Homotopical Aspects of Torsion Theories. Mem Amer Math Soc, Vol 188, No 883. Providence: Amer Math Soc, 2007

4
Chen J M. Cotorsion pairs in a recollement of triangulated categories. Comm Algebra, 2013, 41: 2903–2915

5
Cline E,Parshall B, Scott L. Derived categories and Morita theory. J Algebra, 1986, 104: 397–409

6
Cline E, Parshall B, Scott L. Finite-dimensional algebras and highest weight categories. J Reine Angew Math, 1988, 391: 85–99

7
Dickson S E. A torsion theory for Abelian categories. Trans Amer Math Soc, 1966, 121: 223–235

8
Franjou V, Pirashvili T. Comparison of abelian categories recollements. Doc Math, 2004, 9: 41–56

9
Gentle R. T.T.F. theories in abelian categories. Comm Algebra, 1988, 16: 877–908

10
Happel D, Reiten I, Smalø S O. Tilting in Abelian Categories and Quasitilted Algebras. Mem Amer Math Soc, Vol 120, No 575. Providence: Amer Math Soc, 1996

11
Iyama O, Yoshino Y. Mutation in triangulated categories and rigid Cohen-Macaulay modules. Invent Math, 2008, 172: 117–168

12
Jans J P. Some aspects of torsion. Pacific J Math, 1965, 15: 1249–1259

13
Juteau D. Decomposition numbers for perverse sheaves. Ann Inst Fourier (Grenoble), 2009, 59: 1177–1229

14
Kuhn N J. Generic representations of the finite general linear groups and the Steenrod algebra II. K-Theory, 1994, 8: 395–428

15
Kuhn N J. A stratification of generic representation theory and generalized Schur algebras. K-Theory, 2002, 26: 15–49

16
Lin Y N, Wang M X.From recollement of triangulated categories to recollement of abelian categories. Sci China Math, 2010, 53: 1111–1116

17
Lin Z Q, Wang M X. Koenig's theorem for recollements of module categories. Acta Math Sinica (Chin Ser), 2011, 54: 461–466 (in Chinese)

18
Liu Q H, Vitória J, Yang D. Gluing silting objects. Nagoya Math J, 2014, 216: 117–151

19
Pirashvili T I. Polynomial functors. Trudy Tbiliss Mat Inst Razmadze Akad Nauk Gruzin SSR, 1988, 91: 55–66

20
Psaroudakis C. Homological theory of recollements of abelian categories. J Algebra, 2014, 398: 63–110

21
Psaroudakis C, Skartsæterhagen Ø, SolbergØ. Gorenstein categories, singular equivalences and finite generation of cohomology rings in recollements. Trans Amer Math Soc (Ser B), 2014, 1: 45–95

22
Psaroudakis C, Vitória J. Recollements of module categories. Appl Categ Structures, 2014, 22: 579–593

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