关于$D(G)^c$的分次中心
On the graded center of $D(G)^c$
AI总结：
本文研究局部 pro-$p$群$G$对应的光滑$G$表示导出范畴中紧对象子范畴的分次中心，对无真开中心化子的$p$-进李群$G$模局部幂零元确定该中心并给出应用。
AI中文摘要：
设$D(G)$为$k$向量空间上光滑$G$表示的导出范畴，其中$G$是局部 pro-$p$群，$k$是特征为$p$的域。本文主要关注紧对象子范畴的分次中心$Z^*(D(G)^c)$及其变体。当$G$为无真开中心化子的$p$-进李群时，我们模局部幂零元完全确定该中心并给出若干应用。
英文摘要：
Let $D(G)$ denote the derived category of smooth $G$-representations on $k$-vector spaces, where $G$ is a locally pro-$p$ group and $k$ is a field of characteristic $p$. In this paper we are primarily interested in the graded center of the subcategory of compact objects $Z^*(D(G)^c)$ and variants thereof. When $G$ is a $p$-adic Lie group, without proper open centralizers, we completely determine this center modulo locally nilpotent elements and give various applications.
