Math 283Z: Foundations of non-abelian Chabauty

Harvard Spring 2023

The non-abelian Chabauty method of Minhyong Kim is one of the premier methods for computing rational or integral points on curves in practice. This course will give a thorough description of the foundations of the method and the theoretical ingredients it combines, and will conclude with an overview of some computations of rational or integral points. A course summary can be found here.

Lecture notes

These are copies of the notes I used for the lectures. Please feel free to contact me via email if you have any comments, queries or corrections. The eventual aim is to write these up properly into a book -- watch this space!
  • Lecture 1: Descent and Chabauty--Coleman.
  • Lecture 2: Groupoids and the profinite etale fundamental group.
  • Lecture 3: Unipotent and pro-unipotent groups.
  • Lecture 4: The pro-unipotent etale fundamental group I: Malcev completion.
  • Lecture 5: The pro-unipotent etale fundamental group II: the Tannakian formalism.
  • Lecture 6: The Galois action on the etale fundamental group.

Problems sheets