On the notion of order in the stable module category [Elektronische Ressource] / vorgelegt von Martin Langer

On the notion of order in the stable module categoryDissertationzurErlangung des Doktorgrades (Dr. rer. nat.)derMathematisch-Naturwissenschaftlichen Fakult atderRheinischen Friedrich-Wilhelms-Universit at Bonnvorgelegt vonMartin LangerausMarburgBonn, 2009Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakultat derRheinischen Friedrich-Wilhelms-Universiatt Bonn1. Referent: Prof. Dr. Stefan Schwede2. Referent: Prof. Dr. Catharina StroppelTag der Promotion: 03.11.2009Diese Dissertation ist auf dem Hochschulschriftenserver der ULB Bonnhttp://hss.ulb.uni-bonn.de/diss_online elektronisch publiziert.Erscheinungsjahr: 2009ContentsOn the notion of order in the stable module categoryMartin LangerAbstractThe notion of order in triangulated categories, as introduced by Schwede, is in-vestigated in the case of the stable category of kG-modules, where k is a eld ofcharacteristicp andG is a nite group. For Tate cohomology classes of even degree,we obtain bounds on the-order which are amazingly similar to corresponding resultson the p-order in the stable homotopy category.On our way we introduce a power operationP on Tate cohomology which serves1as an obstruction for the -order to be larger than its minimal possible value. Fur-thermore, it enables us to compute certain higher Massey products explicitly.Contents1 Prerequisites 61.1 The stable module category . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.