Title: On the class groups of some Kummer extensions
Speaker: Emmanuel Lecouturier (IMJ-PRG)
Time: 2017-11-27, 14:00-15:30
Place: N818
Abstract: Let N and p be prime numbers \ge 5 such that p divides N-1. Calegari and Emerton, using Mazur's theory of the Eisenstein ideal, showed that if \sum_{k=1}^{(N-1)/2} is a p-th power modulo N, then the p-primary part of the class group of Q(N^{1/p}) is not cyclic. We shall give a rather elementary proof of this result, and give more results about this class group and the class group of the cyclotomic eld Q(\zeta_p,\zeta_N). We will make the link between these results and our results on the Eisenstein ideal.