#### Vol. 2, 2019

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Explicit computations in Iwasawa theory

### Reinier Bröker, David Hubbard and Lawrence C. Washington

Vol. 2 (2019), No. 1, 137–153
##### Abstract

We give two algorithms to compute layers of the anticyclotomic ${ℤ}_{3}$-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.

##### Keywords
anticyclotomic, Iwasawa theory, nonmaximal order
Primary: 11R23
Secondary: 14K22
##### Supplementary material

Magma code to compute the examples discussed