Arakelov invariants, Belyi’s theorem, and Szpiro’s small points conjecture

Here you will find notes on Arakelov invariants, Belyi's theorem, and Szpiro's small points conjecture for the lectures given at Chalmers University of Gothenburg from April 4th until April 15th. The notes were taken by Amos Turchet.


  1. Belyi's Theorem Notes
  2. Effective Shafarevich theorems for elliptic curves Notes
  3. Arakelov's intersection Pairing Notes
  4. Discriminant bound: Applications of Arakelov theory Notes
  5. Lang-Vojta's conjecture and Shafarevich-type finiteness theorems Notes
  6. Effective Shafarevich, Szpiro's small points conjecture, effective Mordell Notes


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