Finiteness conjecture for the fundamental group of the regular locus

Let $M$ be a projective irreducible symplectic variety. The regular locus $M_\mathrm{reg}$ is the smooth locus of $M$.

Finiteness conjecture. The fundamental group $\pi_1(M_\mathrm{reg})$ is finite.

This expectation concerns the topology of singular irreducible symplectic varieties and would strengthen the known finiteness of the algebraic fundamental group of the regular locus. Its general status is not specified here.