Weber's class number problem and p--rationality in the cyclotomic Z^-extension of Q
Weber's class number problem and p--rationality in the cyclotomic Z^-extension of Q
Let K:=Q(l^n), n≥0, be the nth layer in the cyclotomic Z_l-extension of Q. It is conjectured that, for all l and n, K is principal (especially for l=2, a conjecture due to Weber). Many studies (Ichimura--Morisawa--Nakajima--Okazaki...) go in this direction, as the Miller use of the Cohen--Lenstra--Martinet heuristics. Nevertheless, we …