论文标题
代数自动形式和超舒张表示的一致性
Congruences of algebraic automorphic forms and supercuspidal representations
论文作者
论文摘要
让$ g $是一个完全真实的现场$ f $，这是Archimedean Places的紧凑型Modulo中心。我们发现Modulo在$ g（\ Mathbb a_f）$上的任意自态形式的空间与P p $ g $ g $ G $ G $ G $ G $ G $ G $ G $ G $ G $ G $ G（\ Mathbb A_F）$的任意功率和具有超舒张组件的自称形式的自动形式。我们说明了如何将这种一致性应用于Galois代表的构建。 我们的证明基于P-ADIC组表示的类型理论，将[Arxiv：1506.04022，第7节]中GL（2）的原型概述推广到一般还原群。我们展示了许多新的超级刺激类型，这些类型由任意小的紧凑型开放子组及其特征组成。我们期望这些独立兴趣的结果能够进一步申请。例如，我们将Emerton-Paškūnas的结果扩展到了超舒张点的密度，从确定的统一群体到上述$ g $。
Let $G$ be a connected reductive group over a totally real field $F$ which is compact modulo center at archimedean places. We find congruences modulo an arbitrary power of p between the space of arbitrary automorphic forms on $G(\mathbb A_F)$ and that of automorphic forms with supercuspidal components at p, provided that p is larger than the Coxeter number of the absolute Weyl group of $G$. We illustrate how such congruences can be applied in the construction of Galois representations. Our proof is based on type theory for representations of p-adic groups, generalizing the prototypical case of GL(2) in [arXiv:1506.04022, Section 7] to general reductive groups. We exhibit a plethora of new supercuspidal types consisting of arbitrarily small compact open subgroups and characters thereof. We expect these results of independent interest to have further applications. For example, we extend the result by Emerton--Paškūnas on density of supercuspidal points from definite unitary groups to general $G$ as above.
