论文标题
阿尔巴内斯地图，用于开放代数空间
Albanese maps for open algebraic spaces
论文作者
论文摘要
我们表明，对于一个分离和有限类型的每个代数空间，其亲密关系被连接和降低，对帕拉 - 阿布尔的品种存在普遍的形态。后者是在某些地面延伸后获取Abelian品种的结构的方案。这概括了从代数品种到阿贝尔品种的普遍形态的经典结果。我们的证明依赖于适当情况的相应事实，以及小组方案的结构特性，通过改变来删除奇异性和ind-objects。事实证明，阿尔巴尼人品种的形成随着普遍同态的基础变化而形成。我们还对代数曲线和代数群的阿尔巴内斯图进行了详细的分析，并特别强调了不完善的地面场。
We show that for each algebraic space that is separated and of finite type over a field, and whose affinization is connected and reduced, there is a universal morphism to a para-abelian variety. The latter are schemes that acquire the structure of an abelian variety after some ground field extension. This generalizes classical results of Serre on universal morphisms from algebraic varieties to abelian varieties. Our proof relies on corresponding facts for the proper case, together with the structural properties of group schemes, removal of singularities by alterations, and ind-objects. It turns out that the formation of the Albanese variety commutes with base-change up to universal homeomorphisms. We also give a detailed analysis of Albanese maps for algebraic curves and algebraic groups, with special emphasis on imperfect ground fields.
