论文标题
理想的相对下降和原理化
Relative desingularization and principalization of ideals
论文作者
论文摘要
在特征零中，我们构建了对数方案的对数正常形态的理想的相对原则化，并使用它来构造形态的对数正常降低。这些结构相对典型甚至起作用，相对于对数的规则形态和任意基础变化。相对典型性意味着，原理化需要对基数进行足够的非规范修改，并且一旦选择了该过程，该过程就是规范。结果，我们通过任意估值环推断出可半降低定理。在另一个我们正在进行的工作中，在适当的形态主义的情况下，将在规范上解决同样的问题。
In characteristic zero, we construct relative principalization of ideals for logarithmically regular morphisms of logarithmic schemes, and use it to construct logarithmically regular desingularization of morphisms. These constructions are relatively canonical and even functorial with respect to logarithmically regular morphisms and arbitrary base changes. Relative canonicity means, that the principalization requires a fine enough non-canonical modification of the base, and once it is chosen the process is canonical. As a consequence we deduce the semistable reduction theorem over arbitrary valuation rings. In another our work in progress, the same problems will be solved canonically in the case of proper morphisms.
