What kind of prerequisites would be required for [Inter-Universal] Teichmuller theory or at least the closest generally known area near Mochizuki's work? (Starting from undergraduate math).
I'd assume something like this – though of course I don't know enough to say myself or I would not be asking.I'm writing these as more modules than subjects, I know that if I were listing subjects some would be contained in others.
$\textbf{Undergraduate}$:
Basic Abstract Algebra
Basic Linear Algebra
Galois Theory
Basic Algebraic Number Theory
Basic Algebraic Geometry
Basic Homological Algebra
Basic Theory of Elliptic Curves
$\textbf{Graduate}$:
Category Theory
Homological Algebra
Sheaf Theory
Algebraic Number Theory
Algebraic Geometry
Elliptic Curves
Am I right in my rough assessment? What else would be required? Any analysis? No clue about the tags or even if this is the right place for the question, if not could I have another site recommended?
Best Answer
Classical Teichmuller theory is a topic in complex analysis. So you would need complex analysis and probably real analysis before that. Depending on the approach you take to Teichmuller theory, some knowledge of manifolds and differential geometry would also be helpful. That's really all you need to pick up an introduction to the subject.
However, I fear you are really asking about Interuniversal Teichmuller Theory, which is an entirely different subject.
Edit: Regarding your edit, you will need everything you listed (and much more). (I'm not a number theorist, but everything you listed is the essential to the study of modern arithmetic geometry.)