Arithmetic level raising conjecture for unitary Shimura varieties

Let $\mathfrak{m}$ be a maximal ideal of the Hecke algebra, and assume Hypotheses~ and~. The relevant special fibre is denoted by ${{\Sh}_{1,n-1}^{{\rm{ss}}}}$, its ambient Shimura variety by ${{\Sh}_{1,n-1}}$, and $\overline{{\Sh}}_{1,n-1}$ denotes its base change to an algebraic closure. Let $k_\lambda$ be the coefficient field and let $\operatorname{Ch}^1$ and $\operatorname{H}_{\acute{e}t}$ denote the corresponding higher Chow group and étale cohomology group. Arithmetic level raising conjecture. Under the stated hypotheses, the level raising map

$${\rm{Ch}}^1({{\Sh}_{1,n-1}^{{\rm{ss}}}},1,k_\lambda)_{\mathfrak{m}}\longrightarrow {\rm{H}}^1(\mathbb{F}_{p^2},{\rm{H}}_{\acute{e}t}^{2n-2}(\overline{{\Sh}}_{1,n-1},k_\lambda(n))_{\mathfrak{m}})$$

is surjective. This is presented as the arithmetic level raising theorem for the relevant unitary Shimura varieties; the supplied text does not establish the conjectural surjectivity.