Iwasawa theory of class groups in the case $p=2$

Abstract: Let $K$ be a $CM$ number field and $K_\infty$ be its cyclotomic $Z_p$-extension with intermediate layers $K_n$. If $p$ is odd we get a decomposition in plus and minus parts of the class group and it is well known that the ideal lift map from $K_n$ to $K_{n+1}$ is injective on the minus part of the class group. For $p=2$ this is in general not true. We will provide a different definition of the minus part and explain how inherits properties that are known for $p>2$. If time allows we will also present an application of these results to compute the $2$ class group of the fields $K_n$ for certain base fields explicitely. Part of this is joint work with M.M. Chems-Eddin.

number theory

Audience: researchers in the topic

Algebra and Number Theory Seminars at Université Laval