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

TL;DR

This paper discusses S. Leroy's approach to the nilpotent case of the Shafarevich conjecture, utilizing higher Albanese manifolds, and extends the proof to the Kähler setting independently of prior work.

Contribution

It introduces a new proof strategy for the nilpotent case of the Shafarevich conjecture based on higher Albanese manifolds, applicable in the Kähler context.

Findings

Leroy's proof is largely independent of Katzarkov's work.

The approach extends to the Kähler setting.

The method relies on higher Albanese manifolds by R. Hain.

Abstract

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.