Integral Swan class conjecture

Let $U$ and $V$ be as in the paper, let $\mathcal F$ be the locally constant constructible sheaf under consideration, and let $\zeta_{p^\infty}$ denote the group of all $p$-power roots of unity. The integral Swan class conjecture asserts that the Swan class $\operatorname{Sw}_U\mathcal F$ lies in the image of

$$F_0G(\partial_{V/U}U)\longrightarrow F_0G(\partial_{V/U}U)_{\mathbb Q(\zeta_{p^\infty})}.$$

The text states that this conjecture is proved when $\dim U_K\leq 1$; it remains unresolved in the generality stated there.