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Construction of maximal unramified p-extensions for given Galois groups

组织者

刁晗生 , 胡悦科 , 埃马纽埃尔·勒库图里耶 , 凯撒·鲁普

演讲者

克里斯蒂安·梅尔

时间

2023年08月21日 10:00 至 11:00

地点

Tsinghua-Jingzhai-105

摘要

About a decade ago, Manabu Ozaki (Waseda University) established the following result: given a finite p-group G, there exists a totally imaginary number field K for which the Galois group of its p-Hilbert tower is isomorphic to G. In collaboration with Farshid Hajir (UMASS) and Ravi Ramakrishna (Cornell University), we have revisited and streamlined Ozaki's proof, which allowed us to relax the condition on the signature of K and to control the degree and ramification of K/Q. In this lecture, I will provide the key elements of our proof.