AI 中文总结
该研究证明离散赋值环分式域上满足特定模型条件的射影几何正规簇的阿尔巴内塞簇具有半阿贝尔约化，并将Fontaine与Abrashkin的经典定理推广到奇异代数几何情形。
AI 中文摘要
设X_K是离散赋值环（DVR）分式域上的射影几何正规簇。我们证明：若X_K存在一个射影模型，其特殊纤维在余维1处至多有结点，则阿尔巴内塞簇Alb_{X_K/K}在同一基上具有半阿贝尔约化。作为应用，我们将经典的Fontaine与Abrashkin关于Z上阿贝尔概型的不存在性定理推广到奇异情形。例如，若平坦射影Z-概型X具有正规且几何连通的纤维，则H^1(X_Q, O_{X_Q})=0。
英文摘要
Let X_K be a projective geometrically normal variety over the fraction field of a DVR. We show that if X_K admits a projective model whose special fibre has at worst nodes in codimension one, then the Albanese variety Alb_{X_K/K} has semi-abelian reduction over the same base. As an application, we extend the classical nonexistence theorem of Fontaine and Abrashkin for abelian schemes over Z to the singular setting. For instance, if a flat projective Z-scheme X has normal and geometrically connected fibres, then H^1(X_Q, O_{X_Q})=0.
