Abstract:
Fargues conjectured that one can view the local Langlands
conjecture over nonarchimedean fields as a geometric Langlands conjecture
on the Fargues-Fontaine curve. As a partial progress report on our joint
work with Fargues, the goal of this talk will be to formulate a
categorical form of this conjecture. Defining the relevant category of
l-adic sheaves requires some innovations in the l-adic formalism, related
to the theory of condensed mathematics and solid abelian groups recently
delevoped with Clausen.
