Explicit computations in Iwasawa theory

Abstract

We give two algorithms to compute layers of the anticyclotomic ${\mathbf{Z}}_3$-extension of an imaginary quadratic field. The first is based on complex multiplication techniques for nonmaximal orders; the second is based on Kummer theory. As an illustration of our results, we use the mirroring principle to derive results on the structure of class groups of nonmaximal orders.

to appear in proceedings of ANTS 13