Mathematical Sciences: Problems in Number Theory

这项研究涉及数学对象之间的幂等关系。它推广和统一了R.Brauer关于类数的工作和R.Accola关于黎曼曲面亏格的工作。这项研究将把这些幂等关系与数域上交换簇的Birch-Swinnerton-Dyer猜想所涉及的量联系起来。这项研究属于代数数论的一般领域。它涉及作用于数学对象的几何变换群及其子群。这些变换群动作决定数值不变量，特别是幂等关系。在这种情况下，研究人员一方面将几何对象与算术对象联系起来。这些链接提供了对几何学和数论的见解。

This research concerns idempotent relations between mathematical objects. It generalizes and unifies the work of R. Brauer on class numbers and R. Accola on genera of Riemann surfaces. The research will relate these idempotent relations to the quantities involved in the Birch-Swinnerton-Dyer conjecture for abelian varieties over number fields. The research is in the general area of algebraic number theory. It concerns geometric transformation groups and their subgroups acting on mathematical objects. These transformation group actions determine numerical invariants and, in particular, idempotent relations. In this context, the researchers link geometric objects on one hand and arithmetic objects on the other hand. These links provide insights into both the geometry and the number theory.