Campana's cotangent-dimension equality conjecture

Let $X$ be a compact connected Kähler manifold and let $p>0$. Write

$$\nu_p(X):=\nu(X,\Omega_X^p),\qquad \kappa_p(X):=\kappa(X,\Omega_X^p).$$

The cotangent-dimension equality conjecture. One has

$$\nu_p(X)=\kappa_p(X).$$

This extends the canonical-bundle equality to all exterior powers of the cotangent bundle; the paper does not establish it in general.