Mathematical Sciences: Problems in Number Theory

该奖项继续支持主要研究者的 研究“数学对象之间的幂等关系”。 本研究是对Brauer以往关于 类数和Accola关于Riemann曲面的亏格。 这 研究，设置在有限型群计划的背景下， 整数，探索某些结构的兼容性 例如Birch-Swinnerton-Dyer和Tate的那些， 群环中的幂等关系 这项研究是在数论的一般领域。 Number 理论是世界上最古老的研究分支之一。 数学科学 它涉及的基本结构， 整数、整数的扩展和基本结构 他们所处的田地。 研究工具需要 分析几何和代数的复杂结合

This award continues support for the principal investigator's research on 'idempotent relations between mathematical objects'. This research generalizes and unifies the past work of Brauer on class numbers and of Accola on genera of Riemann surfaces. This research, set in the context of group schemes of finite type over the integers, explores the compatibility of certain conjectures such as those of Birch-Swinnerton-Dyer and of Tate having idempotent relations in group rings. This research is in the general area of number theory. Number theory is one of the oldest branches of research in the mathematical sciences. It concerns the basic structure of the integers, extensions of the integers, and the fundamental structure of the fields in which they lie. Research tools require a sophisticated blend of analysis, geometry, and algebra.