Ideal Class Groups of Number Fields in $\mathbb{Z}_p$-Extensions

Ideal Class Groups of Number Fields in

Z_{p}

-Extensions

Organizers

Yong Suk Moon , Koji Shimizu

Speaker

Xiu Wu Zhu

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

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

Z_{p}

-extensions. In this talk, we will review known results and outline the proofs for some examples.