In this post we will develop the notion of unramified morphisms, in their various guises.

In this post we will be assuming the reader is familiar with the (relative) cotangent sheaf. If not, I suggest they first read chapter 21 of Vakil’s *Foundations of Algebraic Geometry* or II.8 of Hartshorne. I’ll try to be explicit when I can though, and reference the needed theorems, and sometimes be overly hand-holdy with computations.