Kerz–Esnault–Wittenberg p-adic cycle-class conjecture

Let $A$ be a henselian discrete valuation ring of characteristic zero with residue field of characteristic $p$ and function field $K$. Let $X$ be smooth and projective of relative dimension $d$ over $\operatorname{Spec}(A)$, let $X_1$ be its special fiber, and let $X_n$ be the thickenings of $X_1$. Assume the Gersten conjecture for the Milnor $K$-sheaf $\mathcal{K}^M_{n,X}$. Kerz–Esnault–Wittenberg conjecture. The restriction map

$$\operatorname{res}:\mathrm{CH}^{d}(X)/p^r\rightarrow "\operatorname{lim}_n" H^{d}(X_1,\mathcal{K}^M_{d,X_n}/p^r)$$

is an isomorphism.

This predicts that codimension-$d$ Chow classes modulo $p^r$ are completely detected by the compatible classes on infinitesimal thickenings of the special fiber; the supplied text gives no resolution status.