关于光滑部分函子
On the Smooth Part Functor
摘要：
设$G$是紧$p$ -adic解析群，$k$是域正特征标.我们证明了对于$k$ -向量空间$V$上的$G$的每一个光滑表示，每一个1-上循环$G\to V$都是连续的。我们推导出光滑部分函子的第一个导出函子在光滑表示上为零。作为推论，我们得到光滑表示的扩张是自动光滑的。
英文摘要：
Let $G$ be a compact $p$-adic analytic group and $k$ a field positive characteristic. We prove that for every smooth representation of $G$ on a $k$-vector space $V$, every 1-cocycle $G\to V$ is continuous. We deduce that the first derived functor of the smooth part functor vanishes on smooth representations. As a corollary, we obtain that extensions of smooth representations are automatically smooth.
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