Chinburg–Reid–Stover conjecture for once-punctured torus bundles

Let $M$ be a hyperbolic once-punctured torus bundle, let $\widetilde{C}$ denote the relevant character-curve component, and let $\mathcal{A}_{k(\widetilde{C})}$ be its tautological Azumaya algebra. Suppose that $\mathcal{A}_{k(\widetilde{C})}$ does not extend to an Azumaya algebra over $\widetilde{C}$. Let $\frak{C}$ denote the set of irreducible representations under consideration. Chinburg–Reid–Stover conjecture for once-punctured torus bundles. There exists an infinite set of representations $\{\rho_i\}\subset\frak{C}$, where each $\rho_i$ is the holonomy of a distinct $p_i/q_i$ hyperbolic Dehn filling of $M$, and an infinite sequence of distinct rational primes $\ell_i$ such that the non-invariant quaternion algebra associated to $\rho_i$ ramifies at a finite prime lying over $\ell_i$. Moreover, the $\rho_i$ can be taken to be $n_i/0$-fillings for some strictly monotone sequence of natural numbers $\{n_i\}$. This sharpens the conjecture of Chinburg, Reid, and Stover for hyperbolic knot complements to the once-punctured torus bundle setting; the source notes that the first provable evidence was obtained for the knot $7_4$, while the general assertion remains open.