Morava $E$-theory of filtered colimits
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- by Mark Hovey PDF
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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.References
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Additional Information
- Mark Hovey
- Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
- Email: hovey@member.ams.org
- Received by editor(s): February 14, 2006
- Published electronically: May 8, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2342007