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Local cohomology of ${BP_{*}BP}$-comodules

Published online by Cambridge University Press:  25 February 2005

Mark Hovey  and
Neil Strickland
Mark Hovey
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, CT 06459, USA. E-mail: hovey@member.ams.org
Neil Strickland
Affiliation:
Department of Pure Mathematics, University of Sheffield, Sheffield, S3 7RH, United Kingdom. E-mail: N.P.Strickland@sheffield.ac.uk
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Abstract

Given a spectrum $X$, we construct a spectral sequence of $BP_{*}BP$-comodules that converges to $BP_{*}(L_{n}X)$, where $L_{n}X$ is the Bousfield localization of $X$ with respect to the Johnson–Wilson theory $E(n)_{*}$. The $E_{2}$-term of this spectral sequence consists of the derived functors of an algebraic version of $L_{n}$. We show how to calculate these derived functors, which are closely related to local cohomology of $BP_{*}$-modules with respect to the ideal $I_{n + 1}$.

Keywords

comodulelocalizationderived functorlocal cohomologyBrown–Peterson homologybordism55N2255P6016W30
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 90 , Issue 2 , March 2005 , pp. 521 - 544
Copyright
2005 London Mathematical Society

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