Browsing by Author "Benson, Dave"
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- ItemModule categories for group algebras over commutative rings(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2012) Benson, Dave; Iyengar, Srikanth B.; Krause, Henning; Stevenson, GregWe develop a suitable version of the stable module category of a finite group G over an arbitrary commutative ring k. The purpose of the construction is to produce a compactly generated triangulated category whose compact objects are the finitely presented kG-modules. The main idea is to form a localisation of the usual version of the stable module category with respect to the filtered colimits of weakly injective modules. There is also an analogous version of the homotopy category of weakly injective kG-modules and a recollement relating the stable category, the homotopy category, and the derived category of kG-modules.
- ItemStratifying modular representations of finite groups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2008) Benson, Dave; Iyengar, Srikanth B.; Krause, HenningWe classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context. Others include new proofs of the tensor product theorem and of the classification of thick subcategories of the finitely generated modules which avoid the use of cyclic shifted subgroups. Along the way we establish similar classifications for differential graded modules over graded polynomial rings, and over graded exterior algebras.