Shioda's conjecture on transcendental lattices at supersingular primes

Let $L$ be a number field and let $Z$ be a singular K3 surface over $L$. A prime $\mathfrak{p}$ of $L$ is supersingular if $Z/L_{\mathfrak{p}}$ is supersingular, meaning that $\rho(Z/\overline{L}_{\mathfrak{p}})=22$. Let $T_Z$ be the transcendental lattice of $Z/L$, and define

$$T_{\mathfrak{p}}=NS(Z/\overline{L}_{\mathfrak{p}})\cap NS(Z/\overline{L})^\bot.$$

Shioda's conjecture. If $\mathfrak{p}$ is a supersingular prime, then the two lattices $T_Z$ and $T_{\mathfrak{p}}$ are similar.

This compares the rank-two transcendental lattice in characteristic zero with the orthogonal complement of the geometric Néron–Severi group after supersingular reduction. The paper states that it will verify this conjecture for the singular K3 surface under consideration.