The categorical form of Fargues' conjecture

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.