For aspherical normal complex algebraic varieties, a virtually nilpotent fundamental group is forced to be virtually two-step nilpotent.
Quasi-projective nilmanifolds.arXiv preprint arXiv:2601.16433,
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Topology of higher Albanese maps and aspherical varieties with nilpotent fundamental group
For aspherical normal complex algebraic varieties, a virtually nilpotent fundamental group is forced to be virtually two-step nilpotent.