Appears in collection : New Structures and Techniques in $p$-adic Geometry

I will introduce a perspective on Igusa stacks that can be interpreted as providing a uniformization of the $p$-adic Shimura variety. Using deformation theory and $p$-adic Hodge theory, I will discuss how this uniformization can be pinned down uniquely. As a consequence, we can deduce that Igusa stacks are canonical objects that are unique.