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arXiv · 2304.02622

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

Kenta Suzuki·Yujie Xu
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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.

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Kenta Suzuki, Yujie Xu. 2023-04-05. The explicit Local Langlands Correspondence for $\mathrm{GSp}_4$, $\mathrm{Sp}_4$ and stability (with an application to Modularity Lifting). https://arxiv.org/abs/2304.02622

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