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BIMSA-YMSC Tsinghua Number Theory Seminar
Construction of maximal unramified p-extensions for given Galois groups
Construction of maximal unramified p-extensions for given Galois groups
Organizers
Hansheng Diao
, Yueke Hu
, Emmanuel Lecouturier
,
Cezar Lupu
Speaker
Christian Maire
Time
Monday, August 21, 2023 10:00 AM - 11:00 AM
Venue
Tsinghua-Jingzhai-105
Abstract
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.