Functoriality in Function Fields

本提案的目标是研究功能域案例中的功能原则。起点是朗兰兹的论文“超越内窥镜”，贝林森和德林菲尔德的猜想，以及最近对基本引理的证明，PI对基本引理的证明起到了至关重要的作用。这些元素之间的紧密联系将为函数字段情况下的通用功能提供一条新的道路，并将为进一步研究数字字段情况提供方向。基于PI最近在证明基本引理（朗兰兹计划的一个中心问题）的某些情况方面的成功，该奖项的研究项目为代数几何和表示理论领域的年轻研究人员提供了一系列新的深刻而令人兴奋的问题。

The goal of this proposal is to investigate the functoriality principle in the function field case. The starting points are Langlands' paper 'Beyond Endoscopy', Beilinson and Drinfeld's conjecture and the recent proof of the Fundamental Lemma to which the PI contributed in a crucial way. Strong ties among these elements will provide a new road to general functoriality in the function field case and will give direction to further investigation in the number field case as well.Building on the PI's recent success in proving certain cases of the Fundamental Lemma, a central question in the Langlands program, the research program in this award offers a new set of deep and exciting problems for young researchers in the domain of algebraic geometry and representation theory.