复形的相对射影性与Green对应
Relatively Projectivity and the Green correspondence for complexes
摘要：
我们研究了复形范畴的格林对应，包括同伦范畴和导出范畴。对应是定义在有限群$G$上的范畴与定义在子群$H$上的范畴之间的等价，子群$H$通常是$G$的$p$ -子群的正规化子。我们提出了一个基本公式，用于确定何时模或复形的范畴具有格林对应，并将其应用于许多例子。在某些情况下等价是三角范畴的等价，在特殊情况下等价是张量三角范畴的等价。
英文摘要：
We investigate a version of the Green correspondence for categories of complexes, including homotopy categories and derived categories. The correspondence is an equivalence between a category defined over a finite group $G$ and the same for a subgroup $H$, often the normalizer of a $p$-subgroup of $G$. We present a basic formula for deciding when categories of modules or complexes have a Green correspondence and apply it to many examples. In several cases the equivalence is an equivalence of triangulated categories, and in special cases it is an equivalence of tensor triangulated categories.
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