Semistable Reduction Problems, and Uniformity Problems in Arithmetic Geometry

阿布拉莫维奇9700520 在这个项目中，主要研究者将研究半稳定约化问题，利用de Jong的Alteration方法，Abramovich和de Jong的Torifying Blowup，以及Kempf，Knudsen，Mumford和Saint-Donat的Toroidal Geometry。 他将致力于推广他的结果纤维权力的对数情况下，并继续研究稳定积分点的交换品种，使用紧模空间的阿列克谢夫和中村。 这个项目福尔斯属于算术几何的一般领域，这是一个融合了两个最古老的数学领域：数论和几何的主题。 这种结合已被证明是非常富有成效的，最近解决了几代人的问题。 在它的许多后果是新的纠错码。 这种代码对现代计算机和光盘都是必不可少的。

Abramovich 9700520 In this project, the principal investigator will study semistable reduction problems, making use of the Alteration method of de Jong, the Torifying Blowup of Abramovich and de Jong, and Toroidal Geometry of Kempf, Knudsen, Mumford and Saint-Donat. He will work on generalizing his results on fibered powers to the logarithmic case, and continue the study of stably integral points on abelian varieties, using the compactified moduli spaces of Alexeev and Nakamura. This project falls into the general area of arithmetic geometry, a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers and compact disks.