论文标题
用于超几何滑轮的几何兰兰兹
Geometric Langlands for hypergeometric sheaves
论文作者
论文摘要
广义超几何滑轮是具有显着特性的穿刺射射线线上的刚性局部系统。他们的研究起源于Riemann在Euler-Gauss超测量功能上的开创性工作，并已涌入一个活跃的领域，并与许多数学领域有联系。在本文中，我们构建了Hecke特征概述，其特征值是不可还原的局部系统，从而证实了超晶格几何兰兰兹的中心猜想。关键的新概念是超几何自动化数据的概念。我们证明，这种自动数据通常是刚性的（从Zhiwei yun的意义上），并用超几何滑束识别所得的Hecke特征值。在驯服案例中，超几何自动型数据的定义涉及mirabolic亚组，而在野外，可半介绍（但不一定是稳定的）向量来自主要等级干预。
Generalised hypergeometric sheaves are rigid local systems on the punctured projective line with remarkable properties. Their study originated in the seminal work of Riemann on the Euler--Gauss hypergeometric function and has blossomed into an active field with connections to many areas of mathematics. In this paper, we construct the Hecke eigensheaves whose eigenvalues are the irreducible hypergeometric local systems, thus confirming a central conjecture of the geometric Langlands program for hypergeometrics. The key new concept is the notion of hypergeometric automorphic data. We prove that this automorphic data is generically rigid (in the sense of Zhiwei Yun) and identify the resulting Hecke eigenvalue with hypergeometric sheaves. The definition of hypergeometric automorphic data in the tame case involves the mirabolic subgroup, while in the wild case, semistable (but not necessarily stable) vectors coming from principal gradings intervene.
