A global Hartl–Pink 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.

algebraic geometrynumber theory

Audience: researchers in the topic

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Boston University Number Theory Seminar