论文标题
相对投影率和复合物的绿色对应关系
Relatively Projectivity and the Green correspondence for complexes
论文作者
论文摘要
我们研究了复合物类别的绿色对应的版本，包括同型类别和派生类别。该通信是在有限组$ g $上定义的类别与子组$ h $相同的类别之间的等价性，通常是$ g $的$ p $ -subgroup的函数。我们提供了一个基本公式，用于决定何时何时模块或复合物具有绿色对应关系，并将其应用于许多示例。在某些情况下，等效性是三角类别的等效性，在特殊情况下，它等于张量三角类别。
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.
