Mathematical Sciences: Moduli of Abelian Varieties

本研究将研究具有层次结构的整数上的交换格式的模堆栈。它还将研究极化阿贝尔簇的模空间的不同分量在特征为p0的域上的交集。本研究研究被称为阿贝尔簇的数论-代数几何对象。这是对数论中试图求解丢番图方程的研究对象的几何解释，即整数形式的多项式方程的解。诺曼博士在这一领域是一位非常有深度的工作者，到目前为止，他已经开始了这个项目，并取得了非常有希望的结果。这项工作应该会带来非常令人兴奋的进一步结果。

This research will study the moduli stacks of abelian schemes over the integers with level structures. It will also investigate the intersections of the different components of the moduli space of polarized abelian varieties over a field of characteristic p 0. This research studies the number theoretic-algebraic geometric object called an abelian variety. This is the geometric interpretation of the object one studies in number theory in attempting to solve diophantine equations, i.e. solutions of polynomial equations in integers. Dr. Norman is a very deep worker in this area who has already embarked on this project with very promising results so far. This work should lead to very exciting further results.