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Moscow Mathematical Journal, 2011, Volume 11, Number 4, Pages 723–803
DOI: https://doi.org/10.17323/1609-4514-2011-11-4-723-803
(Mi mmj440)
 

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
Full-text PDF Citations (9)
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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
Bibliographic databases:
Document Type: Article
MSC: 18G99
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 723--803
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\crossref{https://doi.org/10.17323/1609-4514-2011-11-4-723-803}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2918295}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000300368300004}
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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