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Morava $ E$-theory of filtered colimits


Author: Mark Hovey
Journal: Trans. Amer. Math. Soc. 360 (2008), 369-382
MSC (2000): Primary 55N22, 55P42, 55T25
DOI: https://doi.org/10.1090/S0002-9947-07-04298-5
Published electronically: May 8, 2007
MathSciNet review: 2342007
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Abstract: Morava $ E$-theory $ E_{n*}^{\vee }(-)$ is a much-studied theory in algebraic topology, but it is not a homology theory in the usual sense, because it fails to preserve coproducts (resp. filtered homotopy colimits). The object of this paper is to construct a spectral sequence to compute the Morava $ E$-theory of a coproduct (resp. filtered homotopy colimit). The $ E_{2}$-term of this spectral sequence involves the derived functors of direct sum (resp. filtered colimit) in an appropriate abelian category. We show that there are at most $ n-1$ (resp. $ n$) of these derived functors. When $ n=1$, we recover the known result that homotopy commutes with an appropriate version of direct sum in the $ K(1)$-local stable homotopy category.


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Additional Information

Mark Hovey
Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
Email: hovey@member.ams.org

DOI: https://doi.org/10.1090/S0002-9947-07-04298-5
Received by editor(s): February 14, 2006
Published electronically: May 8, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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