Conjecture on irreducibility of the Bloch variety for periodic Schrödinger operators

Let $V$ be a periodic potential and let $B(V)$ denote its Bloch variety. An analytic set is irreducible if it cannot be represented as the union of two nonempty proper analytic subsets. Bloch-variety irreducibility conjecture. The Bloch variety $B(V)$ is irreducible modulo periodicity. This conjecture concerns the global analytic structure of Bloch varieties and is part of the broader expectation that Bloch and Fermi varieties for periodic Schrödinger operators are irreducible. The supplied text gives no resolution status.