Principal version of the Chebotarev density theorem and class group

讲座时间 Datetime: 2021年11月12日，星期五， 10:00-11:30

地点 Venue: 腾讯会议，360 685 416

报告人 Speaker:  马宁 博士

单位 Affiliation: 纽约州立大学布法罗分校

报告摘要 Abstract:

Let K/k be a finite Galois extension of number fields, and let H_K be the Hilbert class field of K. We find a way to verify the nonsplitting of the Hilbert exact sequence by finite calculation. Our method is based on the study of the principal version of the Chebotarev density theorem, which represents the density of the prime ideals of k that factor into the product of principal prime ideals in K. We also find explicit equations to express the principal density in terms of the invariants of K/k. In particular, we prove that the group structure of the ideal class group of K can be determined by reading the principal densities.