In the study of the arithmetic local Langlands correspondence, there is a conjecture that was recently (in this decade) formulated by Fargues.

I can't even concisely state the conjecture so I will defer this to the answerers who will presumably do a much better job of it. I can, however, give a link to a paper by Fargues from which, with sufficient effort, you should be able to extract understanding of the conjecture.

Can you show us "a mathematical path" one can walk along to arrive at the conjecture, starting from the facts which you might expect an average third-year graduate student in specializing in arithmetic geometry or automorphic forms to know? A sort of a one-page (or so) explanation of why one should believe the geometrization conjecture. It would be also nice if you explain what is the relation to the geometric Langlands theory as developed by Gaitsgory and others (my guess is that they are only similar in the name but that is just a guess).

The paper of Fargues already provides a 46-page explanation but it would much easier to follow if one has a specific picture in mind to begin with. There is probably more than one answer to this question (all roads lead to Rome!) but there are not that many people in the world who understand the geometrization conjecture so if we get at least one answer that would be fortunate.