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

Convexit\'e holomorphe du rev\^etement de Malcev d'apr\`es S. Leroy