Gluing of endopermutation modules

摘要

We introduce the notion of Frobenius-friendly categories and obtain the slash functors on these categories. LetGbe a finitep-group. We give a local construction of the-stable category of a big enough Frobenius-friendly categoryof-modules: an endopermutation-module ingives rise, via slash functors, to a family of endopermutation-modules, whereQruns over non-trivial subgroups ofG, together with certain isomorphisms. Conversely, the data of a suitable compatible family of endopermutation-modulescomes from an endopermutation-module inunique up to isomorphism in the-stable category.