Non-cuspidality outside the middle degree of l-adic cohomology of the Lubin-Tate tower

On non-abelian Lubin-Tate theory via vanishing cycles

We give a purely local proof, in the depth 0 case, of the result by Harris-Taylor which asserts that the local Langlands correspondence for GL_n over a p-adic field K realizes itself inside the vanishing cycle cohomology of the deformation space of formal O_K-modules of height n. Our proof is given by establishing the direct geometric link with the Deligne-Lusztig theory for GL_n over the residue field.

Multivariable Lubin-Tate (ϕ,Γ)-modules and filtered ϕ-modules

We define some rings of power series in several variables, that are attached to a Lubin-Tate formal module. We then give some examples of (ϕ,Γ)-modules over those rings. They are the global sections of some reflexive sheaves on the p-adic open unit polydisk, that are constructed from a filtered ϕ-module using a modification process. We prove that we obtain every crystalline (ϕ,Γ)-module over those rings in this way.

Théorie de Lubin-Tate non abélienne l-entière

For two distinct primes p and l, we investigate the Z_l-cohomology of the Lubin-Tate towers of a p-adic field. We prove that it realizes some version of Langlands and Jacquet-Langlands correspondences for flat families of irreducible supercuspidal representations parametrized by a Z_l-algebra R, in a way compatible with extension of scalars. When R is a field of characteristic l, this gives a cohomological realization of the Langlands-Vigneras correspondence for supercuspidals, and a new proof of its existence. When R runs over complete local algebras, this provides bijections between deformat…

Lubin-Tate模空间平展覆盖中的局部解析表示

Locally analytic representations in the étale coverings of the Lubin-Tate moduli space

本文将Lubin-Tate模空间上自同构群诱导局部解析表示的结果推广至$\boldsymbol{\mathbb{Q}_p}$有限扩张赋值环上的形式模形变及带Drinfeld level-$m$结构的形变空间情形，并确定了对应截面空间的局部有限向量空间的结构。

Geometric approach to the explicit local Langlands correspondence

We propose a geometric strategy of giving explicit description of the Langlands parameter of an irreducible supercuspidal representation of GL(n) over a non-archimedean local field. The key is to compare the cohomology of an affinoid in the Lubin-Tate space at infinite level and that of the reduction of its formal model. As examples, we treat the cases of depth 0 supercuspidal representations and simple supercuspidal representations.

Correspondance locale de Langlands et monodromie des espaces de Drinfeld

The conjecture stated by Carayol in [{\em Non-abelian Lubin-Tate theory.} Automorphic forms, Shimura varieties and $L$-functions, vol II: 15--39, Academic Press,1990] predicted that the {\em supercuspidal part} of the l-adic cohomology of the moduli spaces classifying certain formal groups introduced by Drinfeld would provide a simultaneaous "realization" of Langlands and Jacquet-Langlands local correspondences for {\em supercuspidal} representations of $GL_d$. By works of Harris, Boyer, Harris-Taylor and Hausberger, this conjecture is now proved. On another hand, recent works by Boyer and Fal…

关于Drinfeld空间商栈的pro-étale上同调

On the pro-étale cohomology of quotient stacks of Drinfeld spaces

该研究聚焦p进域上Drinfeld空间商栈的pro-étale上同调问题，借助Lubin-Tate塔与Drinfeld塔的同构及已有Drinfeld空间p进上同调结果，给出两类商栈ℓ进与p进pro-étale上同调的显式描述，并应用于计算GLₙ(ℚₚ)的连续群上同调。

p-adic局部解析表示的Jacquet-Langlands函子

A Jacquet-Langlands functor for $p$-adic locally analytic representations

本文研究了无限层局部Shimura品种的局部解析理论，证明了不同周期sheaves在无限层的局部解析向量与p-adic李群作用无关，并展示了Jacquet-Langlands函子与局部解析向量及李代数中心字符的兼容性。

四元数Shimura曲线完成余弦学中局部解析向量的研究

Locally analytic vectors in the completed cohomology of quaternionic Shimura curves

本文研究四元数Shimura曲线完成余弦学中局部解析向量的性质及其与Hecke特征值的关系，并探讨其在晶体质地情况下的Hodge滤波检测问题。