Siyan Daniel Li-Huerta (MPIM Bonn): Close fields and the local Langlands correspondence

There is a heuristic that, as ramification goes to infinity, p-adic fields tend to function fields. For Galois representations, this was made precise by Deligne, and for representations of p-adic groups, a similar result was shown by Kazhdan and Ganapathy. We present a proof that this is compatible with Fargues–Scholze’s local Langlands correspondence. The proof relies on carrying out Fargues–Scholze’s construction over the one-point compactification of the natural numbers.

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