About the course
We will take the following question as our motivation: In what sense can a
matrix group with entries in Z/pnZ, with p prime, be
thought of as an algebraic group?
In the first two or three lectures, I'll develop the general theory of Witt
vectors and arithmetic jet spaces (or Greenberg transforms). I'll do this
from the point of view of p-derivations, arithmetic differential
oeprators, and δ-rings, which allows for a clean development parallel
to the geometric theory of usual usual jet spaces. It is due mainly to
André Joyal and Alexandru Buium.
In the remining time, I'll turn to algebraic groups and discuss specific
structures and properties that arise with them. I'll conclude with some
applications and questions.
