John C. Miller
Published 2014-10-10Version 1
For any prime p and any positive integer n, let B(p,n) denote the n-th layer of the cyclotomic Z_p-extension over the rationals. Based on the heuristics of Cohen and Lenstra, and refined by new results on class numbers of particular B(p,n), we provide evidence for the following conjecture: For all primes p and positive integers n, the ideal class group of B(p,n) is trivial.
Minimal relative units of the cyclotomic $\mathbb Z_2$-extension
Cyclic cubic fields whose ideal class group has $n$-rank at least two
Quadratic fields with a class group of large 3-rank
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