On the 2-part of the ideal class group of the cyclotomic Z p -extension over the rationals

摘要

Let p be an odd prime number, and $mbox {boldmath $B$}_{infty}$ the cyclotomic $mbox {boldmath $Z$}_{p}$ -extension over the rationals. We show that the 2-part of the ideal class group of $mbox {boldmath $B$}_{infty}$ is trivial for p500.