Fargues's conjecture, 10 years on

In December 2014, Fargues gave a seminal lecture at MSRI, introducing his revolutionary idea that local Langlands should amount to geometric Langlands on the Fargues-Fontaine curve.
Already in this talk, he conjectured the existence of certain Hecke eigensheaves associated with discrete L-parameters, and predicted some of their properties. In the subsequent 10 years, Fargues's vision has developed into a very wide-ranging and fruitful program which is now on solid technical footing.

Taking advantage of these developments, we will return to Fargues's original setting and formulate an extremely precise refinement of Fargues's eigensheaf conjecture for a very general class of L-parameters, and discuss what is known about it. We will also formulate the so-called magic wand conjecture.