The higher-dimensional continuous Fermi variety irreducibility conjecture

Let $d\geq 3$, let $V_c:\mathbb{T}^d\to\mathbb{C}^d$ be a periodic function, and let $-\Delta_c+V_c$ be the corresponding continuous periodic Schrödinger operator, where $\Delta_c$ is the continuous Laplacian. Let its Fermi variety at energy $\lambda\in\mathbb{C}$ be understood modulo periodicity. Higher-dimensional continuous Fermi variety conjecture. The Fermi variety of $-\Delta_c+V_c$ is irreducible modulo periodicity for every $\lambda\in\mathbb{C}$. The source presents this as motivated by results for discrete operators; no resolution status is given.