On the local constancy of characters

曲线模空间上的Betti自守范畴的局部常性

Local Constancy of the Betti Automorphic Category over the Moduli of Curves

本文采用纯微局部方法证明了曲线模空间上Betti自守范畴的局部常性猜想，该结果不依赖新近确立的Betti几何朗兰兹猜想，还验证了Ben-Zvi与Nadler关于Betti自守范畴仅依赖曲线亏格的猜想。

Asymptotics and local constancy of characters of p-adic groups

In this paper we study quantitative aspects of trace characters $Θ_π$ of reductive $p$-adic groups when the representation $π$ varies. Our approach is based on the local constancy of characters and we survey some other related results. We formulate a conjecture on the behavior of $Θ_π$ relative to the formal degree of $π$, which we are able to prove in the case where $π$ is a tame supercuspidal. The proof builds on J.-K.~Yu's construction and the structure of Moy-Prasad subgroups.

Characters and growth of admissible representations of reductive p-adic groups

We use coefficient systems on the affine Bruhat-Tits building to study admissible representations of reductive p-adic groups in characteristic not equal to p. We show that the character function is locally constant and provide explicit neighbourhoods of constancy. We estimate the growth of the subspaces of invariants for compact open subgroups.