Here we would like to formulate a conjecture which relates the Gromov-Hausdorff limit with non-archimedean geometry, thus giving a pure algebraic description of ${\bf Z}$-affine structure on $B^{sm}$. Let $\overline{{{\bf C}}_{t}^{mer}}=\cup_{m\geq 1}{{\bf C}}_{t^{1/m}}^{mer}$ be the algebraic closure of ${{\bf C}}_{t}^{mer}$. We denote by $\pi_{mer}:X(\overline{{{\bf C}}_{t}^{mer}})\to B$ the map which associates the limiting point (in Gromov-Hausdorff metric) of points $x(t^{1/m})\in X_{t^{1/m}}({{\bf C}})$ as $t^{1/m}\to 0$.

Let ${K}={{\bf C}}((t))$ be the field of Laurent formal series. Then, by extending scalars we obtain an algebraic Calabi-Yau manifold ${X}$ over ${K}$. We denote by ${X}^{an}$ the corresponding smooth ${K}$-analytic space.

Also we make the following conjecture (or better a wish, because it is based on a very thin evidence):