Mathematical Sciences: "L-Adic Representations and Iwasawa Theory"

该奖项支持算术代数的研究 普林斯顿大学的安德鲁·怀尔斯教授的几何学。博士 怀尔斯计划继续他在岩泽理论的研究， 检查与以下项相关联的表示的对称正方形： 一个特定的Hecke特征形。他希望通过这种方式， 攻击格林伯格的论点，这涉及到新定义的 L-adic表示相容族的塞尔默群。 这是算术代数领域的研究 几何学是一门结合了代数和几何学技巧的学科。 几何学和数论在其最初的提法中， 代数几何处理的图形，可以定义在 平面由最简单的方程，即多项式。Number 理论开始于整数， 一个整数被另一个整数整除。这两个主题， 看似相隔甚远，实际上却相互影响， 但在过去的四分之一世纪， 影响力大增。算术领域 代数几何现在使用的技术， 数学，并具有相应的影响力超出其本身 边境

This award supports the research in arithmetic algebraic geometry of Professor Andrew Wiles of Princeton University. Dr. Wiles plans to continue his researches in Iwasawa Theory by examining the symmetric square of a representation associated to a certain class of Hecke eigenforms. In this way, he hopes to attack the Greenberg conjectures, which concern the newly defined Selmer groups of compatible families of L-adic representations. 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.