## Equivariant Riemann—Roch theorem and a BSD-like formula for Hasse—Weil—Artin L-functions over global function fields

2024.04.25- Date
- 2024-05-01 (16:00 ~ 17:30)
- Location
- UNIST Building 108, Room 320

Here’s the seminar schedule for the first week of May 2024.

Speaker: 김완수 (KAIST)

When: 5월 1일 (수요일), 16:00–17:30

Where: 108동 320호 (Reading Room)

Title: Equivariant Riemann—Roch theorem and a BSD-like formula for Hasse—Weil—Artin L-functions over global function fields

Abstract:

Let X be a smooth projective curve over a perfect field of characteristic p>0, and Y be a finite Galois covering of X (possibly allowing ramification). We first review the “refined’’ Riemann—Roch theorem for equivariant vector bundles on Y (due to Nakajima, Köck, and Fischbacher-Weitz & Köck), starting with the modular representation theory of finite groups and local integral normal basis theorem. We then explain how to use it to deduce the p-part of the BSD-like formula for Hasse—Weil—Artin L-functions over global function fields.

This is joint work in progress with Ki-Seng Tan, Fabien Trihan and Kwok-Wing Tsoi.

Thank you.