The top cohomology of principal congruence subgroups of special linear groups over Euclidean number rings

For $R$ a Euclidean number ring, and let ${\mathrm{\Gamma }}_n(p)$ be the level-$p$ principal congruence subgroup of ${\text{SL}}_n(R)$. Borel–Serre showed that the cohomology of ${\mathrm{\Gamma }}_n(p)$ vanishes above a degree $\nu$ that is quadratic in $n$. Let $K$ be the fraction field of $R$, and ${\mathcal{T}}_n(K)$ the Tits building of ${\text{SL}}_n(K)$. For $R=\mathbb{Z}$, Lee–Szczarba asked when ${\text{H}}^{\nu }({\mathrm{\Gamma }}_n(p))$ is isomorphic to ${\tilde{\text{H}}}_{n-2}({\mathcal{T}}_n(K)\mathrm{/}{\mathrm{\Gamma }}_n(p))$, which was answered by Miller–Patzt–Putman. We study a generalized version of Lee–Szczarba’s question. We prove that for a prime $p$ in a Euclidean number ring $R$ with fraction field $K$, that a natural map ${\text{H}}^{\nu }({\mathrm{\Gamma }}_n(p))\to {\tilde{\text{H}}}_{n-2}({\mathcal{T}}_n(K)\mathrm{/}{\mathrm{\Gamma }}_n(p))$ is always surjective, and give a sufficent set of conditions on $p\in R$ that guarantee when this map is an isomorphism.