Some examples of algebraic groups
In this post I want to give a few examples of the known “pathological” behavior of algebraic groups defined over general bases. In particular, this post contains examples of the following.
- A smooth group scheme over a DVR with generic fiber
and special fiber 
, - An affine smooth group scheme
be a connected reductive group over a finite field 
with 
elements, and let 
be the unipotent radical of some Borel 
of 
of 
of …