Derived Mackey functors
Derived Mackey functors
复制标题
派生的 Mackey 函子
DOI：
10.17323/1609-4514-2011-11-4-723-803
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
D. Kaledin
中科院分区：
文献类型：
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作者：
D. Kaledin
对于有限群G，G-Mackey函子构成了一个阿贝尔范畴M（G），它在G-等变稳定同伦的研究中有许多应用.人们会期望导出的范畴$D（M（G））$与$G$-等变稳定同伦范畴的“同调”对应物同样重要。事实并非如此，D（M（G））在很多方面都是病态的.我们提出并研究了一个替代$D（M（G））$的“导Mackey函子”的三角范畴$DM（G）$，它包含$M（G）$但不同于$D（M（G））$.我们证明了$G$-等变稳定同伦范畴的标准特征，如两种类型的不动点函子，与DM（G）范畴有精确的相似之处。
For a finite group $G$, the so-called $G$-Mackey functors form an abelian category $M(G)$ that has many applications in the study of $G$-equivariant stable homotopy. One would expect that the derived category $D(M(G))$ would be similarly important as the "homological" counterpart of the $G$-equivariant stable homotopy category. It turns out that this is not so -- $D(M(G))$ is pathological in many respects. We propose and study a replacement for $D(M(G))$, a certain triangulated category $DM(G)$ of "derived Mackey functors" that contains $M(G)$ but is different from $D(M(G))$. 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 $DM(G)$.