A rational point of $X_{K}^{\text{\rm an}}$ is a point $p\in X^{{\text{\rm an}}}$ satisfying $\mathscr{H}(p)=K$. We denote by $X^{\text{\rm an}}(K)$ the set of rational points of $X^{{\text{\rm an}}}$. More generally, for a complete extension $K^{\prime}$ of $K$, the set of $K^{\prime}$-rational points of $X^{{\text{\rm an}}}$ is defined as $X^{\text{\rm an}}(K^{\prime})=X^{\text{\rm an}}_{K^{\prime}}(K^{\prime})$. There is a map $X^{{\text{\rm an}}}(K^{\prime})\to X^{{\text{\rm an}}}$, defined by the composing the inclusion $X^{{\text{\rm an}}}(K^{\prime})\hookrightarrow X_{K^{\prime}}^{{\text{\rm an}}}$ with the map $X_{K^{\prime}}^{{\text{\rm an}}}\to X_{K}^{{\text{\rm an}}}$ as above. The set of algebraic points of $X^{{\text{\rm an}}}$ is the union of $X^{{\text{\rm an}}}(K^{\prime})$ for all finite extensions $K^{\prime}$ of $K$. Its image in $X^{{\text{\rm an}}}$ is denoted $X^{{\text{\rm an}}}_{{\text{\rm alg}}}$. We have that $X^{{\text{\rm an}}}_{{\text{\rm alg}}}=\{p\in X|\,[\mathscr{H}(p):K]<\infty\}$.