The cyclotomic trace equivalence conjecture for schemes over finite fields

Let $X$ be a nice scheme over $\mathbf{F}_{p}$, let $K(X)$ denote its algebraic $K$-theory spectrum, and let $TC(X,p)$ denote its $p$-typical topological cyclic homology. Cyclotomic trace equivalence conjecture. After $p$-completion, the cyclotomic trace map

$$K(X)\longrightarrow TC(X,p)$$

is a weak equivalence on connective covers. This conjecture predicts that, for schemes over $\mathbf{F}_{p}$, topological cyclic homology provides the noncommutative counterpart of the cohomological side of the crystalline Grothendieck trace formula. Its status is not resolved in the supplied source.