Functional Transcendence in Diophantine Geometry

This minicourse is part of the CMI-HIMR Summer School on Unlikely Intersections in Diophantine Geometry.

Date/Time: August 22 - August 26, 2022

Room: Mathematical Institute, University of Oxford.

Contents: This was the program of the five lectures:

1. Introduction, (functional) transcendence, and complex abelian varieties

2. An axiomatic framework for functional transcendence and weakly special subvarieties and Ax-Lindemann for abelian varieties

3. Abelian schemes and functional transcendence in the universal family

4. The Betti map, the Betti form, and non-degeneracy

5. Sketch of the proof of the Dimitrov-Gao-Habegger bound for the number of rational points on a curve of genus at least 2 over a number field

Material:

• Lecture notes (last updated: 11/04/23, including corrections in Adobe Acrobat comments)