Title: On the Galois structure of units in totally real p-rational fields
Speaker: Donghyeok Lim（韩国教育大学）
Time: Monday, August 25, 2025, 15:00–16:00
Venue: Gewu Building315
Abstract ：The structure of algebraic units as a Galois module is fundamental in number theory. Investigating this structure presents challenges due to the complexities involved in understanding the arithmetic of number fields and the difficulty in classifying integral representations of finite groups. A number field is called p-rational if the Galois group of its maximal pro-p p-ramified extension is a free pro-p group. The concept of p-rationality is known to simplify various problems in number theory. In this talk, we present our recent results on the implications of existing theories on integral representations of finite groups ---such as factor equivalence, regulator constants, and Yakovlev diagrams--- on the structure of algebraic units in totally real p-rational fields. This talk is based on several joint works with Z. Bouazzaoui, D. Burns, A. Kumon, and C. Maire.
