p-ADIC Methods In The Theory Of Algebraic Cycles

Raskind 9700896该奖项支持工作的理论代数循环代数簇p-adically完全领域和代数数域。 主要研究者将定义和研究p进中间雅可比代数簇在一个p进完全域，其中有一个p进的一致化。 预计这些将成为理论中的基本工具。 他还将研究更高的障碍哈塞原则品种代数数域。 代数圈理论是代数几何的一部分，它研究多项式方程组的解。 这是数学中最古老的领域之一，但在过去的30年里，它经历了新思想和基本定理的爆炸。 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.