The p-rank ε-conjecture on class groups is true for towers of p-extensions
The p-rank ε-conjecture on class groups is true for towers of p-extensions
Let p≥2 be a given prime number. We prove, for any number field kappa and any integer e≥1, the p-rank e-conjecture, on the p-class groups Cl_F, for the family F_kappa^p^e of towers F/kappa built as successive degree p cyclic extensions (without any other Galois conditions) such that F/kappa be of …