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HIGHER LIMITS OF FUNCTORS ON CATEGORIES OF ELEMENTARY ABELIAN p–GROUPS

Recently, certain categories based on elementary abelian p-groups (i.e., finite pgroups of the form E ∼= (Cp)) have played an important role as indexing categories for approximating spaces. The construction of approximations to classifying spaces in [JM], and the realization of a certain Dickson algebra as the cohomology algebra of a space in [DW2], both depended on the computation of higher derived functors of inverse limits over such categories. The purpose of this paper is to give a general procedure for doing this involving the Steinberg representation of GLn(Fp). One consequence is an upper bound for the degrees in which higher limits over such categories can be nonvanishing.