Mathematical Sciences: Level Structures on Abelian Varieties

该奖项支持马萨诸塞大学彼得·诺曼教授对阿贝尔变种水平结构的研究。Norman博士的工作将涉及将Abel变元从正特征提升到零特征的问题，以及对Hilbert-Blumenthal变元和Dieudonne理论的研究。这是算术代数几何领域的研究，这是一门结合了代数几何和数论技术的学科。在最初的公式中，代数几何处理的是可以在平面上由最简单的方程定义的图形，即多项式。数论始于整数和一个整数被另一个整数整除等问题。这两个学科看似相距甚远，实际上从最早的时候起就相互影响，但在过去的四分之一个世纪里，相互影响大大增加。算术代数几何领域现在使用了所有现代数学的技术，并在其自身边界之外产生了相应的影响。

This award supports the research on level structures for Abelian varieties of Professor Peter Norman of the University of Massachusetts. Dr. Norman's work will involve the problems of lifting Abelian varieties from positive characteristic to zero characteristic, as well as researches on Hilbert-Blumenthal varieties and Dieudonne theory. This is research in the field of arithmetic algebraic geometry, a subject that combines the techniques of algebraic geometry and number theory. In its original formulation, algebraic geometry treated figures that could be defined in the plane by the simplest equations, namely polynomials. Number theory started with the whole numbers and such questions as divisibility of one whole number by another. These two subjects, seemingly so far apart, have in fact influenced each other from the earliest times, but in the past quarter century the mutual influence has increased greatly. The field of arithmetic algebraic geometry now uses techniques from all of modern mathematics, and is having corresponding influence beyond its own borders.