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This article is cited in 9 scientific papers (total in 9 papers)
Derived Mackey functors
D. Kaledinab a Korean Institute for Advanced Studies, Seoul, Rep. of Korea
b Steklov Math. Institute, Moscow, USSR
Abstract:
For a finite group $G$, the so-called $G$-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.
Received: December 15, 2008; in revised form August 16, 2010
Citation:
D. Kaledin, “Derived Mackey functors”, Mosc. Math. J., 11:4 (2011), 723–803
Linking options:
https://www.mathnet.ru/eng/mmj440 https://www.mathnet.ru/eng/mmj/v11/i4/p723
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