Equivariant Riemann—Roch theorem and a BSD-like formula for Hasse—Weil—Artin L-functions over global function fields
アブストラクト
Let X be a smooth projective curve over a perfect field of characteristic p>0, and Y be a finite Galois covering of X (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.