What’s the point? There’s supposed to be a “curve” \(\Xff\) over \(\QQpadic\) where local Langlands for \(\QQpadic\) should be encoded as geometric Langlands on \(\Xff\), which glues together important period rings from p-adic Hodge theory. Stems from conjectures of Grothendieck wanting to related de Rham cohomology to etale cohomology, and a similar theorem proved by Faltings in the 80s.