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·平克共同开展的一个项目，从定性的角度分析伽罗瓦表示法兼容系统的完整形象。基本的经典问题，即在交换簇上寻找有限阶点的伽罗瓦群，在特殊情况下至少可以追溯到Kronecker，但总体上仍然没有解决。第二个项目更狭隘地关注于寻找数域上中心单代数的哈斯互易定律的n维变体的推广。这项研究属于数论的一般数学领域。数论的历史根源在于对整数的研究，它解决了一些问题，比如一个整数被另一个整数整除的问题。它是数学中最古老的分支之一，出于纯粹的美学原因，人们追寻了许多个世纪。然而，在过去的半个世纪里，它已经成为数据传输和处理以及通信系统等领域的各种应用中不可或缺的工具。

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.