p-ADIC Methods In The Theory Of Algebraic Cycles

这个奖支持在p-根完全域和代数数域上代数变异的代数循环理论方面的工作。主要研究者将定义和研究具有p进均匀化的p进完备域上的代数变量的p进中间雅可比矩阵。预计这些将成为理论的基本工具。他还将研究代数数域上的变量的Hasse原理的更高障碍。代数循环理论是代数几何的一部分，是对多项式方程组解的研究。这是数学中最古老的领域之一，但在过去的三十年里，它经历了新思想和基本定理的爆炸式增长。此外，该理论在编码理论、密码学和工程中也有新的应用。

Raskind 9700896 This award supports work on the theory of algebraic cycles on algebraic varieties over p-adically complete fields and over algebraic number fields. The principal investigator will define and study p-adic intermediate Jacobians for algebraic varieties over a p-adically complete field which have a p-adic uniformization. It is expected that these will be fundamental tools in the theory. He will also study higher obstructions to the Hasse principle for varieties over algebraic number fields. The theory of algebraic cycles is part of algebraic geometry, which is the study of solutions to systems of polynomial equations. This is one of the oldest fields in mathematics, but it has experienced an explosion of new ideas and fundamental theorems over the past thirty years. Also, new applications of the theory have been found to coding theory, cryptography and engineering.