发表机构
Xiamen University Malaysia（厦门大学马来西亚分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究在Fargues-Scholze的范畴局部朗兰兹对应框架下，通过结合几何Satake对应、谱作用与奇点叠操作，提出了Arthur包的三部分猜想性构造，推广了复域上的相关几何构造到ℓ进域情形。
AI 中文摘要
我们在Fargues-Scholze的范畴局部朗兰兹对应（CLLC）框架内，提出了Arthur包的一种猜想性构造。该构造分为三个部分。首先，我们概述了CLLC的核心结论、对应两侧的基础模叠——参数模叠$\text{Par}_G$与$G$-丛模叠$\text{Bun}_G$，以及它与约化p进群表示的关联。接着，我们回顾几何Satake对应，以定义Hecke算子、$\text{Par}_G$上的层对$\text{Bun}_G$上的层的谱作用，并利用偏移数据构造半单参数。最后，我们将Arthur包的几何构造，从在$\text{Par}_G$的正则余法丛上推进摩天大楼层（基于$\text{Par}_G$在$\boldsymbol{\text{C}}$上的情形），推广为$\text{Par}_G$在$\boldsymbol{\text{Q}}_\boldsymbol{\text{ℓ}}$上的奇点叠上的一种猜想性类似操作。
英文摘要
We present a conjectural construction of Arthur packets within Fargues-Scholze's framework for the categorical local Langlands correspondence (CLLC). This construction consists of three parts. We first provide an overview the main statement of the CLLC, the underlying moduli stacks -- $\mathrm{Par}_G$ of parameters and $\mathrm{Bun}_G$ of $G$-bundles -- on the two sides of the correspondence, and its relation to representations of reductive p-adic groups. We then review the geometric Satake correspondence in order to define Hecke operators and the spectral action of sheaves on $\mathrm{Par}_G$ on sheaves on $\mathrm{Bun}_G$, and to construct semisimple parameters using excursion data. Finally, we generalize the geometric construction of Arthur packets from pushing-forward skyscraper sheaves on the regular conormal bundle of $\mathrm{Par}_G$ over $\mathbb C$ to a conjectural analogous operation on the stack of singularities on $\mathrm{Par}_G$ over $\overline{\mathbb Q}_\ell$.
CommentsAs pointed out by Prof Teruhisa Koshikawa, Conjecture 4.8 is ill-formulated. We will address the issue in the near future and provide a correction
