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 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
Mathematical Subject Classification 2010
Primary: 11R23
Secondary: 14K22
Supplementary material

Magma code to compute the examples discussed

Milestones
Received: 19 February 2018
Revised: 9 September 2018
Accepted: 10 September 2018
Published: 13 February 2019
Authors
Reinier Bröker
Center for Communications Research
Princeton, NJ
United States
David Hubbard
Hamilton, NJ
United States
Lawrence C. Washington
Department of Mathematics
University of Maryland
College Park, MD
United States