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Results tagged with derived-categories
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user 75
For questions about the derived categories of various abelian categories and questions regarding the derived category construction itself.
3
votes
Accepted
Projective resolutions of torsion modules
No. In fact, this is as far from true as possible: a finitely generated $\mathbb{Z}/l^n\mathbb{Z}$-module has a finite free resolution iff it is free. To see this, note that a finitely generated $\m …
- 31.2k
17
votes
Homotopy-theoretic derived Morita equivalences
Fernando's answer is excellent, but I can't resist mentioning what is perhaps the simplest counterexample to a generalization to your question. As Fernando says, there are counterexamples if you gene …
- 31.2k
5
votes
$E_\infty$ spectrum corresponding to $\Bbb Z_p$
I don't know whether this actually helps answer your question, but Gereon Quick has done some work on profinite simplicial objects that may be relevant. You might want to poke around his papers a bit …
- 31.2k
7
votes
Accepted
Left orthogonals to compact objects in triangulated categories: existence and "control"?
This happens in spectra. By a theorem of Lin, there are no maps from the Eilenberg-MacLane spectra $H\mathbb{F}_p$ to finite spectra; the proof is an Adams spectral sequence computation using the fac …
- 31.2k