Beilinson's characteristic-cycle direct-image conjecture

Let $k$ be a perfect field, and let $f\colon X\to Y$ be a morphism of smooth schemes over $k$. Assume that every irreducible component of $X$ has dimension $n$ and every irreducible component of $Y$ has dimension $m$. Let $\Lambda$ be a finite field of characteristic $\ell$ invertible in $k$, let ${\cal F}$ be a constructible complex of $\Lambda$-modules on $X$, and write $C=SS{\cal F}$ for its singular support. Assume that $f$ is proper on the support of ${\cal F}$. Characteristic-cycle direct-image conjecture. One has

$$CCRf_*{\cal F}=f_!CC{\cal F}$$

in $\operatorname{CH}_m(f_\circ SS{\cal F})$. This predicts that characteristic cycles commute with proper direct image, strengthening the known inclusion $SSRf_*{\cal F}\subset f_\circ SS{\cal F}$; the supplied source gives no resolution of the conjecture.