Congruences of algebraic automorphic forms and supercuspidal representations

IF 1.8 2区 数学 Q1 MATHEMATICS
Jessica Fintzen, S. Shin
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引用次数: 4

Abstract

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--Paskūnas on density of supercuspidal points from definite unitary groups to general $G$ as above.
代数自同构形式的同余与超三尖体表示
设$G$是全实域$F$上的连通归约群,该域是阿基米德点上的紧致模中心。我们在$G(\mathbb A_F)$上的任意自同构形式的空间与在p处具有超拟素数分量的自同构形式空间之间找到模p的任意幂的同余,条件是p大于$G$的绝对Weyl群的Coxeter数。我们说明了如何将这种同余应用于伽罗瓦表示的构造中。我们的证明是基于p-adic群表示的类型论,将[arXiv:1506.04022,Section 7]中GL(2)的原型情况推广到一般还原群。我们展示了大量由任意小的紧致开放子群组成的新的超尖瓣类型及其特征。我们期望这些独立感兴趣的结果有进一步的应用。例如,我们将Emerton-Paskånas关于超尖点密度的结果从定酉群推广到一般$G$。
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来源期刊
CiteScore
3.10
自引率
0.00%
发文量
7
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