Adelic Problems in Algebraic Number Theory

拉森9701410 该奖项资助迈克尔·拉森教授的研究，他将研究代数数论中的两个问题。 第一个是与理查德·平克共同进行的一个项目，在定性意义上分析伽罗瓦表示的兼容系统的完整图像。基本的经典问题，寻找伽罗瓦群的点的有限秩序的交换品种，至少可以追溯到克罗内克在特殊情况下，但仍然未解决的一般。 第二个项目是更狭窄的重点和关注的搜索推广到n维品种的哈塞的互惠法中心简单代数数领域。 本文的研究属于数论中的一般数学领域福尔斯。 数论有其历史根源，在研究整个数字，解决这样的问题，如那些处理整除一个整数由另一个。它是数学中最古老的分支之一，几个世纪以来，人们纯粹出于美学的原因而追求它。然而，在过去的半个世纪，它已成为一个不可或缺的工具，在不同的应用领域，如数据传输和处理，通信系统。

Larsen 9701410 This award funds the research of Professor Michael Larsen, who will investigate two problems in algebraic number theory. The first is a project undertaken jointly with Richard Pink to analyze in a qualitative sense the full image of a compatible system of Galois representations. The underlying classical problem, finding the Galois group of the points of finite order on an abelian variety, goes back at least to Kronecker in special cases but remains unsolved in general. The second project is more narrowly focused and concerns the search for a generalization to n-dimensional varieties of Hasse's reciprocity law for central simple algebras over number fields. This research falls into the general mathematical field of Number Theory. Number Theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.