第二类群的列表示的有限性
Finitude pour les representations lisses de groupes p-adiques
摘要：
研究了任意p可逆的交换环R中系数为p进群G的光滑表示范畴的基本性质。我们的主要目的是证明Hecke代数是noetherian每当R是;一个问题左开放，因为伯恩斯坦的基本工作R=C。在第一步中，我们证明，这noether属性将遵循从所谓的伯恩斯坦的第二伴随属性之间的抛物函子复表示的推广。然后，攻击这第二个伴随性，我们引入和研究“parahoric函子”之间的表示群的积分点的光滑积分模型G和他们的“Levi”子群。将我们的一般性研究应用于Bruhat-Tits仿射模型，得到了极小抛物群的第二伴随性.对于非极小的抛物子群，我们必须限制到经典群和线性群，并使用与Bushnell-Kutzko和Stevens半单特征标相关的光滑模型.根据Kim和Yu最近的声明，同样的策略也适用于“驯服团体”，使用Yu的通用字符。
英文摘要：
We study basic properties of the category of smooth representations of a p-adic group G with coefficients in any commutative ring R in which p is invertible. Our main purpose is to prove that Hecke algebras are noetherian whenever R is ; a question left open since Bernstein's fundamental work for R=C. In a first step, we prove that this noetherian property would follow from a generalization of the so-called Bernstein's second adjointness property between parabolic functors for complex representations. Then, to attack this second adjointness, we introduce and study "parahoric functors" between representations of groups of integral points of smooth integral models of G and of their "Levi" subgroups. Applying our general study to Bruhat-Tits parahoric models, we get second adjointness for minimal parabolic groups. For non-minimal parabolic subgroups, we have to restrict to classical and linear groups, and use smooth models associated with Bushnell-Kutzko and Stevens semi-simple characters. According to recent announcements by Kim and Yu, the same strategy should also work for "tame groups", using Yu's generic characters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
