The localization of spectra with respect to homology

@article{Bousfield1975TheLO,
  title={The localization of spectra with respect to homology},
  author={Aldridge Knight Bousfield},
  journal={Topology},
  year={1975},
  volume={18},
  pages={133-150}
}
IN [8] WE studied localizations of spaces with respect to homology, and we now develop the analogous stable theory. Let Ho” denote the stable homotopy category of CW-spectra. We show that each spectrum E E Ho” gives rise to a natural E*localization functor ( )E: Ho” -+HoS and n : 1 +( )E. For A E Ho”, v:A-+AE is the terminal example of an E*-equivalence going out of A in Ho”. After proving the existence of ES-localizations, we develop their basic properties and discuss in detail the cases where… Expand
The K-theory localization of an unstable sphere
GIVEN a space or a spectrum X, in [3,4] Bousfield constructs a localization of-X with respect to a generalized homology theory E,( ). An elegant motivation for this construction is presented in [2],Expand
Topological Quillen localization of structured ring spectra
The aim of this short paper is two-fold: (i) to construct a TQ-localization functor on algebras over a spectral operad O, in the case where no connectivity assumptions are made on the O-algebras, andExpand
Complex and real K-theory and localization
The main purpose of this note is to prove some facts about localization (in the sense of Bousfield [S]) of a space X with respect to real and complex K-Theory. In particular we compare the spacesExpand
ON TOWERS APPROXIMATING HOMOLOGICAL LOCALIZATIONS
Our object of study is the natural tower which, for any given map f : A → B and each space X, starts with the localization of X with respect to f and converges to X itself. These towers can be usedExpand
Bousfield localization functors and Hopkins ’ zeta conjecture
This paper arose from attempting to understand Bousfield localization functors in stable homotopy theory. All spectra will be p-local for a prime p throughout this paper. Recall that if E is aExpand
Bousfield Localization Functors and Hopkins' Chromatic Splitting Conjecture
This paper arose from attempting to understand Bousfield localization functors in stable homotopy theory. All spectra will be p-local for a prime p throughout this paper. Recall that if E is aExpand
E*-INJECTIVE SPECTRA AND INJECTIVE
In [13] Ohkawa introduced the notion of the injective hull of spaces and spectra with respect to homology and proved the existence theorem [13, Theorem 1J. Following [13, Definition 1 i)] we call aExpand
Lecture 2 : Spectra and localization
• a sequence of spaces Xn for n ∈ N; • for each n, a map ΣXn → Xn+1. A map of spectra X → Y is an equivalence class of choices of maps Xn → Yn that make the obvious squares commute. Two of these areExpand
Localization and genus in group theory and homotopy theory
To support the development in (1) we combine the works of Adams [1], Casacuberta-Peschke-Pfenniger [7] and chapter I of the present exposition. Thus we arrive at the following pivotal point. TheExpand
Localization with respect to a class of maps I — Equivariant localization of diagrams of spaces
Homotopical localizations with respect to a set of maps are known to exist in cofibrantly generated model categories (satisfying additional assumptions) [4, 13, 24, 35]. In this paper we expand theExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 13 REFERENCES
Localization of CW-complexes and its applications
In the algebraic topology, in particular in the homotopy theory, abelian groups are often treated by being devided into their $p$-primary component” for various primes $p$ . In the homotopy categoryExpand
The order of the image of the $J$-homomorphism
The set üS can be identified with the set of all base point preserving maps of $ into itself. SO(n)> acting on S as R with a point a t infinity, is also a set of base point preserving maps of S ontoExpand
Rational homotopy theory
For i ≥ 1 they are indeed groups, for i ≥ 2 even abelian groups, which carry a lot of information about the homotopy type of X. However, even for spaces which are easy to define (like spheres), theyExpand
Epimorphic extensions of non-commutative rings
The core of a ring
...
1
2
...