On the Fargues--Scholze local Langlands correspondence for Yu's supercuspidals

Abstract: There are several different approaches to the local Langlands correspondence, which can be roughly grouped as "classical", "explicit", and "geometric". Each of these has its own useful features, and it is expected that they all ultimately yield the same correspondence, but this is far from clear. There has been a lot of work by many people comparing the classical and geometric approaches, and some partial work comparing the other two pairs of approaches. I will discuss recent joint work with Tony Feng which is focused on comparing the explicit and geometric approaches due to Kaletha and Fargues--Scholze, respectively. The main recent tools making this comparison possible are Feng's modular functoriality and Scholze's independence of \(\ell\).

number theory

Audience: researchers in the topic

London number theory seminar

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