All Questions
Tagged with localization stable-homotopy
8 questions
3
votes
0
answers
108
views
Localizations of spaces with respect to homology and right properness
Let $E$ be a spectrum (with corresponding homology theory denoted $E_\ast$).
In "Localization of spaces with respect to homology", Bousfield constructed a model category structure on the ...
- 901
30
votes
1
answer
787
views
Is a filtered colimit of rational spaces again rational?
Let me first explain the statement of the question and then give some indication why the answer might be 'yes'.
By a space I mean, say, a simplicial set and by rational I mean rational in the sense of ...
- 383
42
votes
2
answers
2k
views
What is an infinite prime in algebraic topology?
The links between algebraic topology (stable homotopy theory in particular) and number theory are nowadays abundant and fruitful. In one direction, there is chromatic homotopy theory, exploiting the ...
- 4,780
8
votes
2
answers
1k
views
Absence of Maps Between p-local and q-local spectra
Suppose $X$ and $Y$ are spectra (or homotopy classes thereof) such that $X$ is p-local and $Y$ is q-local, for primes $p\neq q$. Is it indeed true then, and if so how would one show that $[X,Y]_\ast=...
- 10.5k
10
votes
1
answer
1k
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Smashing localizations in the category of spectra
Let $E$ be a spectrum. Then $E$ determines an idempotent localization functor $L_E: \mathrm{Sp} \to \mathrm{Sp}$ sending each spectrum to its $E$-localization.
The functor $L_E$ generally does not ...
- 25.6k
8
votes
1
answer
646
views
Is there an obvious reason why p-localization of spectra is a finite localization?
Is there an obvious reason why $p$-localization of spectra is a "finite" localization in the sense of Haynes Miller? In other words, is there an obvious reason why the localizing subcategory (of the ...
- 1,871
6
votes
1
answer
818
views
Spectra and localizations of the category of topological spaces
Can we construct the category of spectra (or maybe just its homotopy category) from the category of pointed topological spaces
using some kind of localization combined with other categorical ...
- 37.8k
3
votes
1
answer
217
views
Does Wolbert's derived equivalence between $E_*^R$-local $R$-modules and $R_E$-modules come from a Quillen equivalence?
Let $R$ be a ring spectrum (in the world of EKMM $S$-modules) and let $E$ be a smashing $R$-module. Denote by $R_E$ the $E_*$-localization of $R$. By a theorem of Wolbert (Theorem 2 in Classifying ...
- 3,184