A global Hartl–Pink curve

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 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.