论文标题
Pro-P $ -IWAHORI共同体的功能性属性
Functorial properties of pro-$p$-Iwahori cohomology
论文作者
论文摘要
假设$ f $是$ \ mathbb {q} _p $，$ g $的有限扩展，是连接还原的$ f $ -group的$ f $ - 点，而$ i_1 $是pro-$ p $ -iwahori $ g $。我们构建两个光谱序列，将$ g $ $ g $的派生函数与来自Pro-P $ -IWAHORI共同体的Hecke模块上的类似函数有关。更具体地说：（1）使用Ollivier-vignéras的结果，我们在Pro-P $ -IWAHORI同胞的抛物线诱导右伴随与Emerton的普通部件的函数之间提供了联系； （2）我们建立了一个“Poincaré二元频谱序列”，该频谱序列与Kohlhaase的较高光滑双重函数有关pro-P $ -IWAHORI的同谋二元性。作为应用程序，我们计算了Hecke模块$ \ textrm {h}^i（i_1，π）$的各种示例。
Suppose $F$ is a finite extension of $\mathbb{Q}_p$, $G$ is the group of $F$-points of a connected reductive $F$-group, and $I_1$ is a pro-$p$-Iwahori subgroup of $G$. We construct two spectral sequences relating derived functors on mod-$p$ representations of $G$ to the analogous functors on Hecke modules coming from pro-$p$-Iwahori cohomology. More specifically: (1) using results of Ollivier--Vignéras, we provide a link between the right adjoint of parabolic induction on pro-$p$-Iwahori cohomology and Emerton's functors of derived ordinary parts; and (2) we establish a "Poincaré duality spectral sequence" relating duality on pro-$p$-Iwahori cohomology to Kohlhaase's functors of higher smooth duals. As applications, we calculate various examples of the Hecke modules $\textrm{H}^i(I_1,π)$.
