We prove a conjecture of Heinloth–Ng？–Yun on the functoriality of Kloosterman sheaves for reductive groups, and calculate the monodromy groups and Newton polygons of these sheaves. This work gives the first example of a p-adic version of geometric Langlands correspondence. This allows us to relate various constructions in the geometric Langlands program.

Publication:

Inventiones mathematicae volume 227, pages997–1092 (2022)

Author:

Daxin Xu

Morningside Center of Mathematics and Hua Loo-Keng Key Laboratory of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Beijing 100049, China School of Mathematical Sciences, University of Chinese Academy of Sciences

e-mail: daxin.xu@amss.ac.cn

Xinwen Zhu

USA Department of Mathematics, California Institute of Technology, Pasadena, CA 91125

e-mail:xzhu@caltech.edu