Local cohomology of BP*BP-comodules
Abstract
In a previous paper, the authors showed that the category of E(n)*E(n)-comodules is a localization of the category of BP*BP-comodules. In this paper, we study the resulting localization functor Ln on the category of BP*BP-comodules. It is an algebraic analogue of the usual topological localization Ln. It is left exact, so has right derived functors Lni. We show that these derived functors are closely related to the local cohomology groups of BP*-modules studied by Greenlees and May; in fact, they coincide with Cech cohomology with respect to In+1. We also construct a spectral sequence of comodules analogous to the Greenlees-May spectral sequence (of modules) converging to BP*(Ln X) whose E2-term involves Lni(BP*X). The proofs require getting a partial understanding of injective objects in the category of BP*BP-comodules.
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