AI 中文总结
针对特征零域\(k\)上有限群的无限族\(U\)，对全局表示导出范畴\(D(U)\)的局部化理想分类，证明其望远镜猜想成立，通过对偶性确立导出 VI - 模相关猜想，还证明了 FI - 模导出范畴的望远镜猜想。
AI 中文摘要
本文针对特征零域\(k\)上有限群的各种无限族\(U\)，对全局表示的导出范畴\(D(U)\)的局部化理想进行分类。这些族包括初等阿贝尔\(p\) - 群、循环\(p\) - 群、素数阶循环群以及平凡群。我们推断这些\(D(U)\)的望远镜猜想成立。特别地，通过庞特里亚金对偶性，我们关于初等阿贝尔\(p\) - 群的结果也确立了导出 VI - 模的望远镜猜想及相应分类。我们还证明了 FI - 模的导出范畴的望远镜猜想成立。
英文摘要
In this paper, we classify the localizing ideals of the derived category D(U) of global representations over a field k of characteristic zero, for various infinite families U of finite groups. These families include elementary abelian p-groups, cyclic p-groups, and cyclic groups of prime order together with the trivial group. We deduce that the telescope conjecture holds for these D(U). In particular, via Pontryagin duality, our results for elementary abelian p-groups also establish the telescope conjecture and the corresponding classification for derived VI-modules. We also prove that the telescope conjecture holds for the derived category of FI-modules.
