Hypergeometric sheaves on reductive groups

Time：Fri., 15:30-16:30, Dec. 12, 2025

Venue：B725, Shuangqing Complex Building A

Organizer：Caucher Birkar，Jia Jia

Speaker：Lei Fu

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，贾甲

Speaker：

Lei Fu (YMSC)

Time：

Fri., 15:30-16:30, Dec. 12, 2025

Venue：

B725, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Title:

Hypergeometric sheaves on reductive groups

Abstract:

We define the hypergeometric exponential sum associated to a finite family of representations of a reductive group over a finite field. We introduce the hypergeometric l-adic sheaf to describe the behavior of the hypergeometric exponential sum. It is a perverse sheaf. Using the theory of the Fourier transform for vector bundles over a general base, we are able to study the hypergeometric l-adic sheaf via the hypergeometric D-module. We apply our results to the estimation of the hypergeometric exponential sum. This is a joint work with Xuanyou Li.

DATEDecember 11, 2025

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