Lie Groups Seminar

Speaker: Siyan Daniel Li-Huerta (MIT)

Title: A global Fargues–Fontaine curve

Abstract: The "fundamental curve" of arithmetic over nonarchimedean local fields is the Fargues–Fontaine curve. You'd think the "fundamental curve" of arithmetic over global function fields is... just the associated curve over $\mathbb{F}q$. In this talk, I will instead advocate for a different "curve", in the spirit of the Fargues–Fontaine curve. I will explain how its moduli stack of bundles is the function field analog of Igusa stacks, as well as the perspective it gives on Langlands duality.