Zariski density of crystalline points on ${\text{GSp}}_{2n}$-valued local deformation rings

We introduce trianguline deformation spaces $X_{\text{tri}}(\bar{\rho })$ for a ${\text{GSp}}_{2n}$-valued residual representation $\bar{\rho }\text{\hspace{0.17em}⁣}:{\mathcal{G}}_K\to {\text{GSp}}_{2n}(k)$, where $k$ is a finite field of characteristic $p>0$ and ${\mathcal{G}}_K$ is the absolute Galois group of a finite extension $K\mathrm{/}{\mathbb{Q}}_p$, and study their properties. We show Zariski density of the crystalline points on the rigid generic fiber ${\mathfrak{X}}_{\bar{\rho }}$ of the framed deformation space of $\bar{\rho }$ under some conditions.