Arnaud Plessis

 

Let V be an algebraic variety over a number field K. In mathematics, diophantine geometry consists to study the set V(K) (the set of points on V with coordinates in K). 

Typical questions about V(K) are : 

 

1) What is its nature (empty, finite, infinite, group ...) ?

2) What about the "size" of its elements ? 

 

Using an intuitive way, I will give a precise definition of the "size", called " height " in the literaure, in the simplest case, namely when V is the multiplicative group (it's the group defined by the equation x^0 = 1, that is V(K)=K*). This height has numerous good properties, that I will state. Finally, I will finish my talk giving some applications, like the Mordell-Weil theorem.