### Citations

186 | Triangulated categories - Neeman - 2001 |

49 |
Thick subcategories of the stable module category’, Fund
- Benson, Carlson, et al.
- 1997
(Show Context)
Citation Context ...l of additive functors. 3Bousfield localization for ordinary stable module categories first appears in [10], and has since proven to be a very powerful tool in the representation theorist’s armoury: =-=[1]-=-, [2] are but two examples. The latter includes more references. There are several subtle, and not so subtle, differences between the ordinary and the relative case. For instance, the direct limit in ... |

41 |
Idempotent modules in the stable category
- Rickard
- 1997
(Show Context)
Citation Context ...egory. We also show that there is a modification one can make so as to recover the idempotent behaviour. 1 Introduction It is now more than a decade since Rickard introduced his idempotent modules in =-=[10]-=-. They arise from performing a Bousfield localization in StMod(kG). Proposition 1.1. Suppose that L ′ is a thick subcategory of stmod(kG). Let L be the smallest localizing subcategory of StMod(kG) con... |

35 | The spectrum of a module category
- Krause
(Show Context)
Citation Context ...an the norm. It would correspond to the class P(w), considered as objects in the module category, being closed under arbitrary direct limits, which is almost never the case. The reader is referred to =-=[7]-=-[Ch.2] for a discussion on definable subcategories for more details on classes of objects that are closed under direct limits. The next example seems far more indicative of the kinds of behaviour one ... |

10 | Bousfield localization for representation theorists, in Infinite length modules - Rickard - 1998 |

8 |
Transfer maps and virtual projectivity
- Carlson, Peng, et al.
- 1998
(Show Context)
Citation Context ...elatively stable category for idempotent modules ∗ M. Grime University of Bristol email: Matt.Grime@bris.ac.uk arXiv:0708.3741v1 [math.RT] 28 Aug 2007 June 2007 Abstract We answer a question posed in =-=[4]-=-, and demonstrate that in general Rickard modules in relatively stable categories are not idempotent modules even if one localizes with respect to a tensor ideal subcategory. We also show that there i... |

5 |
Triangulated categories, adjoint functors and Bousfield localization
- Grime
- 2006
(Show Context)
Citation Context ... relatively projective submodules and is thus zero in stmodw(kG). The proof is not hard, but it is lengthy. For more details, the reader is referred to [7], which originally appears as an appendix in =-=[6]-=-. 4 Bousfield localization in StModw(kG) From the discussion of the preceding section it follows that we have enough compact objects to apply Bousfield localization in StModw(kG), but we are generally... |

4 | Relative projectivity and ideals in cohomology rings - Carlson, Peng - 1996 |

4 | A generalization of projective covers of modules over finite group algebras, unpublished manuscript - Okuyama |

2 |
Direct sum decompositions of infinitely generated modules
- Benson, Wheeler
- 1999
(Show Context)
Citation Context ...additive functors. 3Bousfield localization for ordinary stable module categories first appears in [10], and has since proven to be a very powerful tool in the representation theorist’s armoury: [1], =-=[2]-=- are but two examples. The latter includes more references. There are several subtle, and not so subtle, differences between the ordinary and the relative case. For instance, the direct limit in Mod(k... |

1 |
localizations and stable homotopy theory
- Precovers
(Show Context)
Citation Context ...ective if it is a direct sum (possibly infinite) of finite dimensional modules. Let S be the class of pure projectivekG-modules. Then S ⊕ = stmodw(kG) ⊕ , and one can use the localization theorems of =-=[5]-=-. The answer turns out to depend upon the set theory one uses. 56 Bousfield localizations in stmodw(kG) ⊕ Suppose that instead of looking at finite Bousfield localizations in StModw(kG), we choose to... |

1 |
Finite dimensional modules and perpendicular subcategories. arxiv:0708.3329
- Grime
- 2007
(Show Context)
Citation Context ...inite dimensional object to M must factor through one of the finite dimensional relatively projective submodules. The proof is not hard, but it is lengthy. For more details, the reader is referred to =-=[6]-=-. 4 Bousfield localization in StModw(kG) From the discussion of the preceding section it follows that we have enough compact objects to apply Bousfield localization in StModw(kG), but we are generally... |