p-ADIC Methods In The Theory Of Algebraic Cycles

拉斯金德9700896这个奖项支持在p-完全域和代数数域上的代数簇上的代数圈理论的工作。主要研究人员将定义和研究p-ady完备域上代数簇的p-ady中间雅可比，其中p-ady齐次化是p-ady齐次化的。预计这些将成为该理论的基本工具。他还将研究代数数域上簇的哈斯原理的更高障碍。代数圈理论是代数几何的一部分，是研究多项式方程组的解的学科。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性增长。此外，还发现了该理论在编码理论、密码学和工程中的新应用。

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.