Let K be a non-Archimedean valued field with valuation ring R. Let $C_\eta $ be a K-curve with compact-type reduction, so its Jacobian $J_\eta $ extends to an abelian R-scheme J. We prove that an Abel–Jacobi map $\iota \colon C_\eta \to J_\eta $ extends to a morphism $C\to J$, where C is a compact-type R-model of J, and we show this is a closed immersion when the special fiber of C has no rational components. To do so, we apply a rigid-analytic “fiberwise” criterion for a morphism to extend to integral models, and geometric results of Bosch and Lütkebohmert on the analytic structure of $J_\eta $.

令K为具有评估环R的非阿基米德值域。令$C_\eta $为具有紧凑型约简的K曲线，因此其雅可比行列式$J_\eta $扩展到阿贝尔R方案J。我们证明阿贝尔-雅可比映射$\iota \colon C_\eta \to J_\eta $扩展到态射$C\to J$，其中C是J的紧凑型R模型，并且我们证明了这一点当C的特殊纤维没有有理组分时，是封闭浸没。为此，我们应用态射的刚性解析“纤维”准则扩展到积分模型，以及 Bosch 和 Lütkebohmert 在$J_\eta $解析结构上的几何结果。