创新团队讨论班

系列学术报告

报告人：徐鹏（硕士， p-adic群表示论）

题目： Tame Langlands correspondence for GL(2) over non-Archimedean local fields （II）

时间： 2009年 12月 22 日 （周二） 下午 14：30-16：20

地点： 4号教学楼402多媒体教室

摘要

If F is a non-Archimedean local field, local class field theory induces a canonical bijection between the characters of the multiplicative group of F and the characters of the Weil group of F . For a positive integer n , it turns out that the $n$-dimension analogy of the characters of $F^{times}$ is irreducible smoothrepresentations of GL(n,F).

The local Langlands conjecture for GL(n) predicts the existence of a canonical bijection between such objects and the n -dimensional semisimple representations of the Weil group of F , thus it generalizes local class field theory. This conjecture has now been completely proved.

The goal of these lectures is to give a brief introduction to the local constrction of Langlands correspondence for GL(2) , given by Bushnell and Henniart recently. For the sake of simplicity, we avoid the tortuous case of p=2 ( p is the characteristic of the residue field of F), i.e.,we consider here only the tame case $pneq2$. The lectures will also contain some backgrounds.