题目：Stabilization on ideal class groups in potential cyclic towers

报告人：李加宁 山东大学

时间：2025年1月11日（周六）上午9:30-10:30

地点：东区第五教学楼5207教室

摘要：Let $F_\infty/F$ be a $\mathbb{Z}_p$-extension. Suppose it is totally ramified at every ramified prime. Fukuda's stabilization result states that if $A_{0}\cong A_1$, then $A_0\cong A_n$ for $n\geq 1$, where $A_n$ is the $p$-class group of the $n$-th layer.We extend the stabilization result of Fukuda in Iwasawa theory on $p$-class groups in $\mathbb{Z}_p$ or $\mathbb{Z}/p^d\mathbb{Z}$ cyclic towers to potential cyclic towers. A typical example of potential cyclic tower is a radical tower, say $\mathbb{Q}\subset \mathbb{Q}(\sqrt[p]{p})\subset  \\mathbb{Q}(\sqrt[p^2]{p})\subset \cdots$.