3 problems

Let $X$ be a projective manifold, let $L$ be a numerically trivial line bundle, and let … be a non-zero section with $q<\dim X$. A finite étale cover is a finite surjective morphis…

Cohomological Carlson–Toledo conjecture. This natural map is not injective.

Let $M$ be a compact Kähler manifold with infinite fundamental group $\Gamma$. Strong Carlson–Toledo conjecture. There exists a finite étale cover $M'$ of $M$ such that the Hurewic…