# Colloquium abstracts

**C. Gasbarri**

University of Strasbourg, France

March 7, 2012

**On the canonical degree of curves on varieties of general type**: One of the leading conjectures in arithmetic and algebraic geometry is the Vojta conjecture. The famous abc conjecture is a special case of it and it implies a precise control of the behavior of algebraic points on varieties of general type. Even in the function fields case, although much more then the number field case is known, the main conjecture is widely open. I will report on the conjecture and explain how some Shimura varieties provide some insight on the conjecture.