The explicit Local Langlands Correspondence for ${\mathrm{GSp}}_4$, ${\mathrm{Sp}}_4$ and stability (with an application to Modularity Lifting)

Abstract

We give a purely local proof of the explicit Local Langlands Correspondence for ${\mathrm{GSp}}_4$ and ${\mathrm{Sp}}_4$. Moreover, we give a unique characterization in terms of stability of $L$-packets and other properties. Finally, in the appendix, we give an application of our explicit local Langlands correspondence to modularity lifting.

44 pages