Author:

Gilles Ph. Gnacadja
Department of Mathematics
University of Georgia
Athens, GA 30602-7403, USA

Abstract:

We study phantom maps in the stable module category {\sf StMod}$(kG)$, where
$k$ is a field and $G$ is a finite group. In this paper we almost exclusively
deal with maps out of countably generated modules. We show that the
space ${\StPh}_{kG}(M,N)$ of stabilized phantom maps $M{\ra}N$ has an
expression as a ${\varprojlim}^{1}$ 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 a particular such 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.



Current status:

Preprint (as of November 18 1996).