Determinant formula for virtual Cartier divisors

Let $f:Z\to X$ be a virtual Cartier divisor of derived Artin stacks, and let $\mathcal{F}\in\operatorname{Perf}(Z)$ be a perfect complex of rank $l$. Determinant conjecture. There is an isomorphism

$$\det(f_{*}\mathcal{F})\cong \mathcal{O}_{X}(lZ).$$

This conjecture is presented as a reduction of the discrepancy conjecture and concerns the determinant of the pushforward of a perfect complex along a virtual Cartier divisor. The supplied text gives no resolution of this general statement.