2 problems

Torus-covering conjecture. If $M$ bears a holomorphic connection on $TM$, then $M$ admits a finite unramified covering by a compact complex torus.

Let $X$ be a compact complex manifold of complex dimension $n$, and let $T$ be a closed positive $(1,1)$-current on $X$. Write $T_{ac}$ for its absolutely continuous part and…