Phantom Maps in the Stable Module Category

Author： Gnacadja Gilles  

Publisher： Academic Press

ISSN： 0021-8693

Source： Journal of Algebra, Vol.201, Iss.2, 1998-03, pp. : 686-702

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Abstract

We study phantom maps in the stable module category StMod(kG), where k is a field and G is a finite group. In this article we almost exclusively deal with maps out of countably generated modules. We show that the space PhkG(M, N) of stabilized phantom maps M → N has an expression as a lim1← space which allows some control on its vanishing. Then we present a situation where all maps are phantom and need not be trivial. We provide explicit details for such a particular situation. Finally we construct a universal phantom map. We use it to show that the composite of two phantom maps is trivial and to characterize the modules with no nontrivial outbound phantom maps.

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