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Elsevier, Journal of Pure and Applied Algebra, 1(103), p. 45-59, 1995

DOI: 10.1016/0022-4049(94)00096-2

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Cohomological Bousfield classes

Journal article published in 1995 by Mark Hovey
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

In this paper, we begin the study of Bousfield classes for cohomology theories defined on spectra. Our main result is that a map f:X → Y induces an isomorphism on E(n)-cohomology if and only if it induces an isomorphism on E(n)-homology. We also prove this for variants of E(n) such as elliptic cohomology and real K-theory. We also show that there is a nontrivial map from a spectrum Z to the K(n)-local sphere if and only if .