Let $A$ be an abelian variety of dimension $g$ over the quotient field $K$ of a DVR $R$ which is a subfield of the complex field $\mathbb{C}$. Then by a result of Grothendieck, we know that there is a finite extension $K\subseteq K^{\prime}$ such that the neutral component of the Néron model of $A^{\prime}=A\otimes_{K}K^{\prime}$, i.e., $N(A^{\prime})^{\circ}$ is semiabelian, so it fits in anexact sequence $0\to T^{\prime}\to N(A^{\prime})^{\circ}_s\to B^{\prime}\to 0$, where $T^{\prime}$ is a torus of dimension $r$ and $B^{\prime}$ is an abelian variety of dimension $g-r$ and $N(A^{\prime})^{\circ}_s$ is the special fiber of $N(A^{\prime})$. Let us construct the real torus $U=\mathbb{R}^g/\Lambda^{\prime}$, where $\Lambda^{\prime}=\mathbb{Z}^{g-r}\oplus\Lambda(T^{\prime})$ and $\Lambda(T^{\prime})=\operatorname{Hom}(T^{\prime}, \mathbb{G}_m)$ is the lattice of characters of $T^{\prime}$.
I would like to know if it is true that the complexification of $U_C$ is isomorphic (as a complex torus) to the complexification $A_C$ of $A$.