Class numbers in cyclotomic [formula omitted]-extensions

Abstract

For any prime p and any positive integer n, let Bp,n denote the nth layer of the cyclotomic Zp-extension over the rationals. Based on the heuristics of Cohen and Lenstra, and refined by new results on class numbers of particular Bp,n, we provide evidence for the following conjecture: For all primes p and positive integers n, the ideal class group of Bp,n is trivial.