Convexité holomorphe du revêtement de Malcev d'après S. Leroy

In these notes, we present the strategy employed by S. Leroy to attack the nilpotent case of the Shafarevich conjecture. The projective case was treated in a paper of L. Katzarkov but Leroy's proof is largely independant and works in the K\"ahler setting as well. It is entirely based on the higher Albanese manifolds constructed by R. Hain.