Functoriality in Function Fields

这个建议的目的是调查函域情况下的函性原则。起点是朗兰兹的论文“超越内窥镜”，贝林森和德林费尔德的猜想和最近的基本引理证明，其中PI以关键的方式做出了贡献。这些元素之间的强联系将提供一条新的道路，以一般函的函数域的情况下，并将给予方向，以进一步调查的数域的情况下，以及。建立在PI的最近成功证明某些情况下的基本引理，一个中心问题，在朗兰兹计划，该奖项的研究计划为代数几何和表示论领域的年轻研究人员提供了一系列新的深入和令人兴奋的问题。

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.