A taster of rigid geometry (Pt I: the Tate perspective)

This is the first in a series of 4 posts whose goal is to briefly introduce rigid geometry with a focus on examples. The ultimate goal is to continue this post (and its sequels) with the reader hopefully having a  broad grasp of the rigid geometry of the objects involved.

Objects with no rational models

The goal of this post, which is just a bit of fun between more serious posts/projects, is to discuss some examples of algebro-geometric objects over which have no models over smaller subfields and explain how moduli theory can help clarify their discovery in certain situations.