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Number Theory Lunch Seminar
Ideal Class Groups of Number Fields in $\mathbb{Z}_p$-Extensions
Ideal Class Groups of Number Fields in $\mathbb{Z}_p$-Extensions
Organizers
Speaker
Time
Thursday, November 21, 2024 12:15 PM - 1:00 PM
Venue
A4-1
Abstract
Let $F$ be a number field and $F_\infty$ be a $\mathbb{Z}_p$-extension of $F$. Iwasawa established certain patterns in the behavior of the class groups of the intermediate fields in $F_\infty/F$. Subsequently, many researchers have conducted more detailed studies of the class groups for various choices of $F$ and different types of $\mathbb{Z}_p$-extensions. In this talk, we will review known results and outline the proofs for some examples.