Rational points of modular curves: an arakelovian point of view

Pierre Parent

General methods from diophantine geometry have been very successful in proving finiteness results for points of algebraic curves with values in number fields. Those results however are in general not effective, for deep reasons, and this prevents from proving triviality (and not only finiteness) of relevant sets of rational points. In this talk I will explain how the situation can be much better in the case of modular curves, by using specific arakelovian methods.