On the Picard group of a compact complex nilmanifold (Q795127)

A nilmanifold \(X=G/\Gamma\) is the compact quotient of a nilpotent simply connected Lie group G by a lattice \(\Gamma\). (Examples: tori are the only Kähler ones.) This paper proves, in particular, that if \(\pi:X\to T\) is the Albanese map of X, then \(\pi^*:Pic^ 0(T)\to Pic^ 0(X)\) is biholomorphic, and that \(Pic^ 0(X)\) is of finite index in the kernel of the Bockstein map \(\delta:H^ 1(X,{\mathcal O}^*)\to H^ 2(G/\Gamma,{\mathbb{Z}}).\)