On the notion of order in the stable module category
On the notion of order in the stable module category
Dokument öffnen (948KB)Art der Hochschulschrift
DissertationPrüfungsdatum
03.11.2009Datum der Veröffentlichung
22.12.2009Erstgutachter
Schwede, StefanZweitgutachter
Stroppel, CatharinaMetadaten
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Inhalt
The notion of order in triangulated categories, as introduced by Schwede, is investigated in the case of the stable category of kG-modules, where k is a field of characteristic p and G is a finite group. For Tate cohomology classes ζ of even degree, we obtain bounds on the ζ-order which are similar to corresponding results on the p-order in the stable homotopy category.
On our way we introduce a power operation P1 on Tate cohomology which serves as an obstruction for the ζ-order to be larger than its minimal possible value. Furthermore, it enables us to compute certain higher Massey products explicitly.
On our way we introduce a power operation P1 on Tate cohomology which serves as an obstruction for the ζ-order to be larger than its minimal possible value. Furthermore, it enables us to compute certain higher Massey products explicitly.
Schlagwörter
Kohomologieoperationen, Homotopietheorie, Modulkategorie, Massey Produkt, Triangulierte Kategorie
Klassifikation (DDC)
510 MathematikLanger, Martin: On the notion of order in the stable module category. - Bonn, 2009. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-19445
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-19445
@phdthesis{handle:20.500.11811/4155,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-19445,
author = {{Martin Langer}},
title = {On the notion of order in the stable module category},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2009,
month = dec,
note = {The notion of order in triangulated categories, as introduced by Schwede, is investigated in the case of the stable category of kG-modules, where k is a field of characteristic p and G is a finite group. For Tate cohomology classes ζ of even degree, we obtain bounds on the ζ-order which are similar to corresponding results on the p-order in the stable homotopy category.
On our way we introduce a power operation P1 on Tate cohomology which serves as an obstruction for the ζ-order to be larger than its minimal possible value. Furthermore, it enables us to compute certain higher Massey products explicitly.},
url = {https://hdl.handle.net/20.500.11811/4155}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-19445,
author = {{Martin Langer}},
title = {On the notion of order in the stable module category},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2009,
month = dec,
note = {The notion of order in triangulated categories, as introduced by Schwede, is investigated in the case of the stable category of kG-modules, where k is a field of characteristic p and G is a finite group. For Tate cohomology classes ζ of even degree, we obtain bounds on the ζ-order which are similar to corresponding results on the p-order in the stable homotopy category.
On our way we introduce a power operation P1 on Tate cohomology which serves as an obstruction for the ζ-order to be larger than its minimal possible value. Furthermore, it enables us to compute certain higher Massey products explicitly.},
url = {https://hdl.handle.net/20.500.11811/4155}
}
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