Special Seminar

In my talk I will describe our joint work with David Kazhdan on the global Langlands correspondence over function fields for arbitrary split reductive groups. Our main result asserts that for every pair $(\pi,\omega)$, where $\pi$ is a cuspidal representation of $G$ one of whose local components is a cuspidal Deligne-Lusztig representation, and $\omega$ is a representation of the dual group, there exists a virtual Galois representation $\rho_{\pi,\omega}$, whose $L$-function equals the $L$-function of the pair $(\pi,\omega)$.