
This article is cited in 2 scientific papers (total in 2 papers)
Derived Mackey functors
D. Kaledin^{ab} ^{a} Korean Institute for Advanced Studies, Seoul, Rep. of Korea
^{b} Steklov Math. Institute, Moscow, USSR
Abstract:
For a finite group $G$, the socalled $G$Mackey functors form an abelian category $\mathcal M(G)$ that has many applications in the study of $G$equivariant stable homotopy. One would expect that the derived category $\mathcal D(\mathcal M(G))$ would be similarly important as the “homological” counterpart of the $G$equivariant stable homotopy category. It turns out that this is not so – $\mathcal D(\mathcal M(G))$ is pathological in many respects. We propose and study a replacement for $\mathcal D(\mathcal M(G))$, a certain triangulated category $\mathcal{DM}(G)$ of “derived Mackey functors” that contains $\mathcal M(G)$ but is different from $\mathcal D(\mathcal M(G))$. We show that standard features of the $G$equivariant stable homotopy category such as the fixed points functors of two types have exact analogs for the category $\mathcal{DM}(G)$.
Key words and phrases:
derived, Mackey functor.
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MSC: 18G99 Received: December 15, 2008; in revised form August 16, 2010
Language: English
Citation:
D. Kaledin, “Derived Mackey functors”, Mosc. Math. J., 11:4 (2011), 723–803
Citation in format AMSBIB
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\by D.~Kaledin
\paper Derived Mackey functors
\jour Mosc. Math.~J.
\yr 2011
\vol 11
\issue 4
\pages 723803
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\mathscinet{http://www.ams.org/mathscinetgetitem?mr=2918295}
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http://mi.mathnet.ru/eng/mmj440 http://mi.mathnet.ru/eng/mmj/v11/i4/p723
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This publication is cited in the following articles:

D. B. Kaledin, “Cyclotomic complexes”, Izv. Math., 77:5 (2013), 855–916

Barwick C., “Spectral Mackey Functors and Equivariant Algebraic KTheory (i)”, Adv. Math., 304 (2017), 646–727

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