Rational points of modular curves: an arakelovian point of view
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.